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[Title]
302_m

% 蕶
% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
[Problem]
̖₢ɓB
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% Level1̖BȉLevel7܂œlB
% 1sڂɂ͏ڍאݒ̃^CgB
% 2sڈȍ~ɖƂ̉𓚂B
% Ɖ𓚁C𓚂Ɩ͂PsďB
% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
% ŏprocessƂsC̎̍svZߒĂB
[Level1]
mibCwxj
19܂ł̐ꂽJ[hB
悭1ƂCɂȂm߂B

process
19܂ł̂2C4C6C84ʂ肠B
ċ߂m$\displaystyle \frac{4}{9}$

$\displaystyle \frac{4}{9}$

8Cԋ10C7܂B
狅1oƂom߂B

process
251o25ʂB͂ǂlɊm炵B
̂oꍇ̐8ʂBāC
$\displaystyle \frac{8}{25}$

$\displaystyle \frac{8}{25}$

2̃TCR𓊂ƂCڂ̐ς6ɂȂm߂B

process
SĂ̏ꍇ̐$6 \times 6=36ʂ$B
TCRA̖ڂACB̖ڂBƒ߂ƂCς6ɂȂꍇ\\
(A,B)=(6,1),(3,2),(2,3),(1,6)4ʂBċ߂m\\
$\displaystyle \frac{4}{36}=\displaystyle \frac{1}{9}$

$\displaystyle \frac{1}{9}$

2̃TCRXY𓊂ƂCoڂ̘̐a6ɂȂm߂B

process
SĂ̏ꍇ̐$6 \times 6=36ʂ$B
TCRX̖ڂXCY̖ڂYƒ߂ƂCa6ɂȂꍇ\\
(X,Y)=(5,1),(4,2),(3,3),(2,4),(1,5)
5ʂB
āC߂m
$\displaystyle \frac{5}{36}$

$\displaystyle \frac{5}{36}$

2̃TCR𓯎ɓƂC2Ƃ̖ڂom߂B

process
2̃TCR𓊂Ƃ̑SĂ̖ڂ̏óC$6 \times 6=36$ʂB
2Ƃłꍇ̐́CЕ̃TCR1C3C5CЕ̃TCR1C3C5o΂悢C
$3 \times 3=9$ʂB\\
ċ߂m$\displaystyle \frac{9}{36}=\displaystyle \frac{1}{4}$

$\displaystyle \frac{1}{4}$

3̍d݂𓊂ƂC3Ƃ\łm߂B

process
ׂĂ̏ꍇ̐$2 \times 2 \times 2=8$ʂB
3Ƃ\łꍇ̐1ʂB
ċ߂m$\displaystyle \frac{1}{8}$\\
iʁjd݂̕\om$\displaystyle \frac{1}{2}$B
3̍d݂𓊂鎎s݂͌ɓƗC߂m\\
$\displaystyle \frac{1}{2} \times \displaystyle \frac{1}{2} \times \displaystyle \frac{1}{2}
=\displaystyle \frac{1}{8}$

$\displaystyle \frac{1}{8}$

2̃TCRXY𓊂ƂCoڂ̘̐a5ɂȂm߂B

process
SĂ̏ꍇ̐$6 \times 6=36ʂ$B
TCRX̖ڂXCY̖ڂYƒ߂ƂCa5ɂȂꍇ\\
(X,Y)=(4,1),(3,2),(2,3),(1,4)
4ʂB
āC߂m
$\displaystyle \frac{4}{36}=\displaystyle \frac{1}{9}$

$\displaystyle \frac{1}{9}$

ACBCC \, 3̃RC𓊂ƂC3Ƃ\ɂȂm߂B

process
}̂悤3̃RC̕\Ɨ̏óC$2 \times 2 \times 2=8$ʂB
3Ƃ\ɂȂ̂1ʂȂ̂ŁC߂m$\displaystyle \frac{1}{8}$
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/302_kakuritsu/pic01.tex}
\end{center}

$\displaystyle \frac{1}{8}$

1`20܂ł̐20̃J[h1oƂC3̔{łm͂炩B

process
SĂ̏ꍇ̐20B3̔{$20 \div 3$6B
߂m$\displaystyle \frac{6}{20}=\displaystyle \frac{3}{10}$

$\displaystyle \frac{3}{10}$

3̍d݂𓯎ɓC3Ƃ\ɂȂm߂B

process
ACBCC3̃RĆC\C̏o$2 \times 2 \times 2=8$ʂB
3Ƃ\ɂȂꍇ̐1ʂBāC߂m
$\displaystyle \frac{1}{8}$

$\displaystyle \frac{1}{8}$

2̃TCR𓯎ɐUāCڂom߂B

process
SĂ̏ꍇ̐$6 \times 6=36$ʂBڂoꍇ̐
(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)6ʂBċ߂m
$\displaystyle \frac{6}{36}=\displaystyle \frac{1}{6}$

$\displaystyle \frac{1}{6}$

1`30܂ł̐30̃J[h1oƂC̃J[h̐3̔{łȂm߂B

process
3̔{$30 \div 3 =10$BJ[h1oƂC3̔{łm$\displaystyle \frac{10}{30}=\displaystyle \frac{1}{3}$B
āC3̔{łȂm$1-\displaystyle \frac{1}{3}=\displaystyle \frac{2}{3}$

$\displaystyle \frac{2}{3}$

2̃TCRUƂCoڂ̘a10ɂȂm߂B

process
SĂ̏ꍇ̐$6\times 6=36ʂ$B
TCRCƂB
ڂ̘a10ƂȂ̂\\
$(C)=(6,\,4),(5,\,5),(4,\,6)$3ʂB
āC߂m\\
$\displaystyle \frac{3}{36}=\displaystyle \frac{1}{12}$

$\displaystyle \frac{1}{12}$

2̃TCRXY𓊂ƂCoڂ̘̐a9ɂȂm߂B

process
SĂ̏ꍇ̐$6 \times 6=36ʂ$B
TCRX̖ڂXCY̖ڂYƒ߂ƂCa9ɂȂꍇ\\
(X,Y)=(6,3),(5,4),(4,5),(3,6)
4ʂB
āC߂m
$\displaystyle \frac{4}{36}=\displaystyle \frac{1}{9}$

$\displaystyle \frac{1}{9}$

1̃TCR2UƂA
2ڂ̐1ڂ̐2{ɂȂm߂B

process
2{ɂȂ̂́A\\
(1,2),(2,4),(3,6)3ʂB
āA$\displaystyle\frac{3}{6\times 6}=\displaystyle\frac{1}{12}$

$\displaystyle\frac{1}{12}$

150܂ł̐1ĂJ[h50ƂɁA
̒13Ŋ؂鐔m͉\%B

process
3Ŋ؂鐔́A\\
$50 \div 3=16.\cdots$A16B\\
$\displaystyle\frac{16}{50}\times 100=32$\%

32\%

2̃TCR𓯎ɓƂCu2v̖ځCu6v̖ڂom߂B

process
2̃TCRACBƂBSĂ̏ꍇ̐$6 \times 6=36$ʂB
ӂ̏ꍇ̐(A,B)=(2,6),(6,2)2ʂBāC$\displaystyle \frac{2}{36}=\displaystyle \frac{1}{18}$

$\displaystyle \frac{1}{18}$

4̐ԋ6̔Ă܂B
̒1oƂC1ڂԋC2ڂłm߂B
Co͑܂ɖ߂Ȃ̂ƂB

process
$\displaystyle \frac{4}{10} \times \displaystyle \frac{6}{9}=\displaystyle \frac{4}{15}$

$\displaystyle \frac{4}{15}$

ԋʂ2Cʂ5̍v7̋ʂĂ܂̒ʂ1
oƂCԋʂom߂ȂB

process
$\displaystyle\frac{{}_2 \mathrm{C}_1}{{}_7 \mathrm{C}_1}=
\displaystyle\frac{2}{7}$

$\displaystyle\frac{2}{7}$

1̂2񓊂ƂC
oڂ̘a11ɂȂm߂ȂB

process
oڂ̘a11ƂȂ̂́Ci1ځC2ځj$=(6,5),(5,6)$2ʂł邩C\\
$\displaystyle\frac{2}{6 \times 6}=\displaystyle\frac{1}{18}$

$\displaystyle\frac{1}{18}$

1̂2񓊂ƂC
oڂ̐ςƂȂm߂ȂB

process
oڂ̐ςƂȂ̂́C\\
i1ځC2ځj\\
$=(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)$
9ʂł邩C\\
$\displaystyle\frac{9}{6 \times 6}=\displaystyle\frac{1}{4}$

$\displaystyle\frac{1}{4}$

3̃RC𓯎ɓƂC3Ƃ\o
m߂ȂB

process
3Ƃ\$\bigcirc \bigcirc \bigcirc $1ʂł邩C߂ḿC\\
$\displaystyle\frac{1}{2 \times 2 \times 2}=\displaystyle\frac{1}{8}$

$\displaystyle\frac{1}{8}$

召2̂𓯎ɓƂC
oڂ̐ς3̔{ƂȂm߂ȂB

process
3̔{$6+4+4+4=20$
$\displaystyle\frac{20}{6 \times 6}=\displaystyle\frac{5}{9}$
\begin{figure}[!hbt]\begin{center}
 \includegraphics[width=40mm,clip]{D:/texlive/2018/bin/win32/mathtex/302_kakuritsu/h30m117.eps}
 \end{center}\end{figure} 

$\displaystyle\frac{5}{9}$







[Level2]
mi{CZxj
܂̒ɐԋ6Ɣ4ĂB̒3̋𓯎ɎoƂC
3Ƃłm߂B

process
SĂ̏ꍇ̐$ {}_{10} \rm{C} _3 =\displaystyle \frac{10 \times 9 \times 8}{3 \times 2 \times 1} =120$B
3Ƃłꍇ̐́C$ {}_4 \rm{C} _3 ={}_4 \rm{C} _1=4 $B
ċ߂ḿC$\displaystyle \frac{4}{120}=\displaystyle \frac{1}{30}$\\
iʁj1oƂɑŜ̐C̐C炪AċN̂ŁC
$\displaystyle \frac{4}{10} \times \displaystyle \frac{3}{9} \times \displaystyle \frac{2}{8}
=\displaystyle \frac{1}{30}$

$\displaystyle \frac{1}{30}$

8{̂2{̓肪Ă邭B
1{2ƂC1ڂɓC2ڂɂ͂̏om߂B

process
$\displaystyle \frac{2}{8} \times \displaystyle \frac{6}{7}=\displaystyle \frac{3}{14}$

$\displaystyle \frac{3}{14}$

5{̂2{̓肪Ă邭B
1ڂɃnYC2ڂnYC3ڂɓ̏om߂B
Co͌ɖ߂Ȃ̂ƂB

process
$\displaystyle \frac{3}{5} \times \displaystyle \frac{2}{4} \times \displaystyle \frac{2}{3}=\displaystyle \frac{1}{5}$

$\displaystyle \frac{1}{5}$

3̐ԋC2̔C3̉̓Ă܂B
̒2̋oƂC2Ƃԋłm߂B

process
$\displaystyle \frac{{}_3 \rm{C} _2}{{}_8 \rm{C} _2}=\displaystyle \frac{3 \times 2}{2 \times 1} \div \displaystyle \frac{8 \times 7}{2 \times 1}
=\displaystyle \frac{3}{28}$

$\displaystyle \frac{3}{28}$

3̐ԋC1̔C2̐̓Ă܂B
̒瓯2̋oƂC1ԋC1łm߂B

process
$\displaystyle \frac{{}_3 \rm{C} _1 \times {}_2 \rm{C} _1}{{}_6 \rm{C} _2}
=3 \times 2 \div \displaystyle \frac{6 \times 5}{2 \times 1}=\displaystyle \frac{2}{5}$

$\displaystyle \frac{2}{5}$

5̐1C2C3C4C54̐I4̐ƂC
łm߂B

process
ׂĂ̏ꍇ̐́C\\
${}_5 \rm{P}_4=5 \times 4 \times 3 \times 2 =120$B
̂C\\
$2 \times {}_4 \rm{P}_3=2 \times 4 \times 3 \times 2 =48$B\\
āC߂ḿC
$\displaystyle\frac{48}{120}=\displaystyle\frac{2}{5}$

$\displaystyle\frac{2}{5}$

jq4lCq3l1ɕׂƂC
[ɒjqԊm߂B

process
SĂ̏ꍇ̐́C\\
${}_7 \rm{P}_7=7 \times 6 \times 5 \times 4 \times 3 \times 2 \times=5040$ʂB\\
̂C[ɒjqԏꍇ̐́C\\
${}_4 \rm{P}_2 \times {}_5 \rm{P}_5
=(4 \times 3)\times (5 \times 4 \times 3 \times 2 \times 1)\\
=12 \times 120=1440$ʂB\\
ł邩
$\displaystyle\frac{1440}{5040}=\displaystyle\frac{2}{7}$

$\displaystyle\frac{2}{7}$

jq5lCq5lCv10l2l̈ψIԂƂC
2lƂqI΂m߂ȂB

process
ׂĂ̏ꍇ̐
${}_{10} \rm{C}_2=\displaystyle\frac{10 \times 9}{2 \times 1}=45$ʂB\\
̂C2lƂqI΂ꍇ̐́C\\
${}_5 \rm{C}_2=\displaystyle\frac{5 \times 4}{2 \times 1}=10$ʂB\\
āC2lƂqI΂ꍇ̊ḿC\\
$\displaystyle\frac{10}{45}=\displaystyle\frac{2}{9}$

$\displaystyle\frac{2}{9}$

ԋʂ5Aʂ32oƂɁA
2ƂԋʂɂȂm߂B

process
$\displaystyle \frac{{}_5 \rm{C} _2}{{}_8 \rm{C} _2}
=\displaystyle \frac{5 \times 4}{2 \times 1} \div \displaystyle \frac{8 \times 7}{2 \times 1}
=\displaystyle \frac{5}{14}$\\
iʁj\\
$\displaystyle\frac{5}{8}\times \displaystyle\frac{4}{7}$

$\displaystyle \frac{5}{14}$

150܂ł̐1ĂJ[h50ƂɁA
̒13ł4ł؂鐔m͉\%B

process
12Ŋ؂鐔́A\\
$50 \div 12=4.\cdots$A4B\\
$\displaystyle\frac{4}{50}\times 100=8$\%

8\%

150܂ł̐1ĂJ[h50ƂɁA
̒13܂4Ŋ؂鐔m͉\%B

process
3̔{̐́A$50\div 3=16\cdots$16B\\
4̔{̐́A$50\div 4=12.5$12B\\
12̔{̐́A$50\div 12=4\cdots$4B\\
3܂4̔{́A$16+12-4=24$B\\
$\displaystyle\frac{24}{50}\times 100=48$\%

48\%

150܂ł̐1ĂJ[h50ƂɁA
̒13܂4Ŋ؂Ȃm͉\%B

process
3̔{̐́A$50\div 3=16\cdots$16B\\
4̔{̐́A$50\div 4=12.5$12B\\
12̔{̐́A$50\div 12=4\cdots$4B\\
3܂4̔{́A$16+12-4=24$B\\
3܂4Ŋ؂Ȃ́A$50-24=26$B
$\displaystyle\frac{26}{50}\times 100=52$\%

52\%

ԋ4C
3C
2
܂̒C3̋ʂoƂC
oʂ̐F3Fłm߂ȂB

process
$\displaystyle\frac{4 \times 3 \times 2}{{}_9 \mathrm{C}_3}
=\displaystyle\frac{2}{7}$

$\displaystyle\frac{2}{7}$







[Level3]
mW
1C2C3C44̃J[hׂ4̐ƂC̐4200ȏɂȂm߂B

process
4̃J[h̕ו$ 4 \, ! = 4 \times 3 \times 2 \times 1=24$ʂB\\
4200ȏ́C4213C4231C4321C43124ʂB\\
āC߂m$\displaystyle \frac{4}{24}=\displaystyle \frac{1}{6}$

$\displaystyle \frac{1}{6}$

9l1ɕԂƂC̒AB񂪗ׂ荇ĕԊm߂B

process
9l̕ѕ$ 9 \, ! $ʂB
AB1lƍlƁC8lׂו$ 8 \, ! $ʂB
AB̕ו2ʂł邩C\\
$\displaystyle \frac{8 \, ! \times 2}{9 \, !}=\displaystyle \frac{2}{9}$

$\displaystyle \frac{2}{9}$

1C2C3C44̃J[hׂ4̐ƂC̐2000ȉɂȂm߂B

process
4̃J[h̕ו$4 \, !=4 \times 3 \times 2 \times 1=24$ʂ肠C
2000ȉ̐́C4ڂ1ŁC3C2C12C3C43̃J[hׂ΂悢C
$3 \, != 3 \times 2 \times 1=6$ʂBāC߂m
$\displaystyle \frac{6}{24}=\displaystyle \frac{1}{4}$

$\displaystyle \frac{1}{4}$

ACBCC \, 3̃RC𓊂ƂC1\ɂȂm߂B

process
ACBCC3̃RĆC\C̏o$2 \times 2 \times 2=8$ʂB
1\ɂȂ̂(A,B,C)=(\,,),(,\,),(,\,\)3ʂȂ̂ŁC߂m
$\displaystyle \frac{3}{8}$

$\displaystyle \frac{3}{8}$

1100܂ł̔ԍ1100̃J[hC1oƂC
ԍ2ł͊؂邪6ł͊؂Ȃm߂B

process
SĂ̏ꍇ̐100B2̔{$100 \div 2$50B6̔{$100 \div 6$16B
āu2ł͊؂邪6ł͊؂Ȃvꍇ̐$50-16=34$B
ċ߂ḿC$\displaystyle \frac{34}{100}=\displaystyle \frac{17}{50}$B

$\displaystyle \frac{17}{50}$

jq8lCq10l̒C3l̓ԂIԂƂCjq1lŏq2lƂȂm߂B

process
3l̑Iѕ́C$ {}_{18} \rm{C} _3 $ʂB
jq1l̑Iѕ$ {}_8 \rm{C} _1 $ʂB q1l̑Iѕ$ {}_{10} \rm{C} _2 $ʂ肾C\\
$\displaystyle \frac{ {}_8 \rm{C} _1 \times {}_{10} \rm{C} _2 }{ {}_{18} \rm{C} _3 }
=\displaystyle \frac{15}{34}$

$\displaystyle \frac{15}{34}$

1`13̐1ꂽJ[h13̒2oƂC
2̃J[h̘̐aɂȂm߂B

process
SĂ̏ꍇ̐́C\\
${} _{13}\rm{C}_2=\displaystyle\frac{13\times 12}{2 \times 1}=78$ʂB\\
13̃J[ĥC6C7B
̘aƂȂꍇ̐́Cu2Ƃ̃J[hv̏ꍇƁC
u2Ƃ̃J[hv̏ꍇ邱ƂlāC\\
${}_6 \rm{C}_2+{}_7 \rm{C}_2=15+21=36$ʂB\\
āC߂ḿC\\
$\displaystyle\frac{36}{78}=\displaystyle\frac{6}{13}$

$\displaystyle\frac{6}{13}$






[Level4]
񂯂
ECƌC񂪂񂯂܂B
EC񂪃O[ŏm߂ȂB

process
SĂ̏ꍇ̐́CO[C`LCp[3ނ2lô
$3 \times 3=9$ʂB
̂EC񂪃O[ŏꍇ̐\\
$iECCCj=iO[C`Lj$1ʂB
āC߂m$\displaystyle \frac{1}{9}$

$\displaystyle \frac{1}{9}$

ACBCC3l񂯂ƂC1̂񂯂łɂȂm߂B
C3l̃O[C`LCp[̏óCꂼꓯlɊm炵ƂB

process
ׂĂ̏o$3^3=27$ʂBɂȂ̂́C\\
1FiCCρjF\\
CCς̕וl$ 3 \, !=6$ʂB\\
1FiCCjCiCCjCiρCρCρjF3ʂ\\
v$6+3=9$ʂB
߂ḿC$\displaystyle \frac{9}{27}=\displaystyle \frac{1}{3}$

$\displaystyle \frac{1}{3}$




[Level5]
ȂƂc
肭2{C炭3{łĂ邭B
̂𓯎2{ЂƂCȂƂ1{肭łm߂B

process
5{̂2{Ђꍇ̐́C\\
$ {}_5 \rm{C} _2 =\displaystyle \frac{5 \times 4}{2 \times 1} =10$ʂB
2{Ƃ炭Ђꍇ̐́C\\
$ {}_3 \rm{C} _2 =\displaystyle \frac{3 \times 2}{2 \times 1} =3$ʂB
āC߂m$1-i2{Ƃ炭̊mj=1-\displaystyle \frac{3}{10}=\displaystyle \frac{7}{10}$

$\displaystyle \frac{7}{10}$

1015܂ł̐ꂽJ[h1B
悭ăJ[h2B
2̃J[ĥCȂƂ15̔{łm߂B

process
SĂ̎o
$ {}_6 \rm{C} _2 =\displaystyle \frac{6 \times 5}{2 \times 1} =15$ʂB
̂2Ƃ5̔{łȂo11C12C13C142oꍇ̐ł邩C
$ {}_4 \rm{C} _2 =\displaystyle \frac{4 \times 3}{2 \times 1} =6$ʂB
ċ߂ḿC
$1-\displaystyle \frac{6}{15}=1-\displaystyle \frac{2}{5}=\displaystyle \frac{3}{5}$

$\displaystyle \frac{3}{5}$

TCR3UƂC6ȂƂ1͏om߂B

process
61oȂḿC\\
$\displaystyle \frac{5}{6} \times \displaystyle \frac{5}{6} \times \displaystyle \frac{5}{6}=\displaystyle \frac{125}{216}$
łBłȂm\\
$1-\displaystyle \frac{125}{216}=\displaystyle \frac{91}{216}$

$\displaystyle \frac{91}{216}$

ԋ5Ɣ3܂B
̑܂2̋ʂ𓯎ɎoƂCȂƂ1͐ԋʂłm߂B

process
ʂ̎o$ {}_8 \rm{C} _2 = 28$ʂB2Ƃʂ̎o$ {}_3 \rm{C} _2 = {}_3 \rm{C} _1 = 3$ʂB
߂m$1-\displaystyle \frac{3}{28}=\displaystyle \frac{25}{28}$

$\displaystyle \frac{25}{28}$

2̐ԋC3̔C1̍̓Ă܂B
̒1̋oƂC܂͍om߂B

process
SĂ̏ꍇ̐́C$ {}_6 \rm{C} _1 = 6$ʂB
u܂͍ov̗]ۂ́uԋovłC̏ꍇ̐́C$ {}_2 \rm{C} _1 = 2$ʂB
āC߂m$1-\displaystyle \frac{2}{6}=\displaystyle \frac{2}{3}$

$\displaystyle \frac{2}{3}$

sȑ܂̒ɐԋ4Ɣ6ĂB
̑܂̒3̋ʂoƂCԋʂȂƂ1om߂B

process
uԋʂ1ȏov̗]ۂ́uԋʂ0vȂ킿uʂ3v
߂m$1-\displaystyle \frac{{}_6\rm{C}_3}{{}_{10}\rm{C}_3}
=1-\displaystyle \frac{6\times 5\times 4}{3\times 2 \times 1}\times 
\displaystyle\frac{3\times 2 \times 1}{10\times 9 \times 8}\\
=1-\displaystyle\frac{6\times 5 \times 4}{10\times 9 \times 8}
=1-\displaystyle\frac{1}{6}=\displaystyle\frac{5}{6}$

$\displaystyle\frac{5}{6}$

ԋ6C5̍v11̋Ă܂B
̒瓯4oƂC
ȂƂ1łm߂B

process
u1ȏオv̗]ۂ́u4SĐԋvB\\
SĂ̏ꍇ̐́C\\
${}_{11} \rm{C}_4
=\displaystyle\frac{11\times 10 \times 9 \times 8}{4\times 3 \times 2 \times 1}=330$ʂB\\
4ԋƂȂꍇ̐́C\\
${}_6 \rm{C}_4={}_6 \rm{C}_2
=\displaystyle\frac{6 \times 5}{2 \times 1}=15$ʂB\\
āC߂ḿC\\
$1-\displaystyle\frac{15}{330}=1-\displaystyle\frac{1}{22}=\displaystyle\frac{21}{22}$

$\displaystyle\frac{21}{22}$

114܂ł14̐CقȂ3̐IԂƂC
I΂ꂽ3̐̐ςƂȂm߂B

process
u3̐ρvƂȂ邽߂ɂ́Cu3̐̂ȂƂ1vł΂悢B\\
SĂ̏ꍇ̐́C\\
${}_{14} \rm{C}_3=\displaystyle\frac{14\times 13\times 12}{3 \times 2 \times 1}=364$ʂ\\
u3̐̑SĂvƂȂ̂́C\\
${}_7 \rm{C}_3=\displaystyle\frac{7\times 6 \times 5}{3 \times 2 \times 1}=35$ʂ\\
āC߂ḿC\\
$1-\displaystyle\frac{35}{364}=1-\displaystyle\frac{5}{52}=\displaystyle\frac{47}{52}$

$\displaystyle\frac{47}{52}$

`CaCb3l̐kCAEōim͂ꂼ$\displaystyle\frac{2}{3}$C$\displaystyle\frac{2}{5}$C$\displaystyle\frac{5}{6}$
łB̂ƂȂƂ1l͍im߂ȂB

process
u1lȏ㍇iv̗]ۂ́u0livȂ킿u3lƂsivB\\
āC$1-\displaystyle\frac{1}{3} \times \displaystyle\frac{3}{5} \times \displaystyle\frac{1}{6}=\displaystyle\frac{29}{30}$

$\displaystyle\frac{29}{30}$

O肪4₠B
̖ɂĂƂɓƂC
ȂƂ1͐m߂ȂB

process
u1ȏ㐳v̗]ۂ́u0␳vȂ킿u4svłB\\
$1-\left(\displaystyle\frac{2}{3} \right)^4=
1-\displaystyle\frac{16}{81}=\displaystyle\frac{65}{81}$

$\displaystyle\frac{65}{81}$






[Level6]
mp
2̃TCR𓊂ƂCڂ̐ς20ȏɂȂm߂B

process
SĂ̏ꍇ̐$6 \times 6=36ʂ$B
TCRA̖ڂACB̖ڂBƒ߂ƂC\\
ς20ƂȂꍇ(A,B)$=$(5,4),(4,5)\\
ς24ƂȂꍇ(A,B)$=$(6,4),(4,6)\\
ς25ƂȂꍇ(A,B)$=$(5,5)\\
ς30ƂȂꍇ(A,B)$=$(6,5),(5,6)\\
ς36ƂȂꍇ(A,B)$=$(6,6)\\
$\displaystyle \frac{8}{36}=\displaystyle \frac{2}{9}$

$\displaystyle \frac{2}{9}$

ԋʂ4Cʂ2܂C2̋ʂoƂC
2ƂFɂȂm߂B

process
2ƂԂɂȂḿC\\
$\displaystyle \frac{{}_4 \rm{C} _2}{{}_6 \rm{C} _2}
=\displaystyle \frac{4 \times 3}{2 \times 1} \div \displaystyle \frac{6 \times 5}{2 \times 1}
=\displaystyle \frac{6}{15}$\\
2ƂɂȂḿC\\
$\displaystyle \frac{{}_2 \rm{C} _2}{{}_6 \rm{C} _2}
=1 \div \displaystyle \frac{6 \times 5}{2 \times 1}
=\displaystyle \frac{1}{15}$\\
āC߂ḿC$\displaystyle\frac{7}{15}$\\
iʁj\\
2ƂԂɂȂḿC$\displaystyle\frac{4}{6}\times \displaystyle\frac{3}{5}$\\
2ƂɂȂḿC$\displaystyle\frac{2}{6}\times \displaystyle\frac{1}{5}$\\
āC$\displaystyle\frac{14}{30}=\displaystyle\frac{7}{15}$

$\displaystyle\frac{7}{15}$

ԋʂ5Cʂ3̍v8̋ʂĂ܂̒C
ʂ𓯎2̋ʂoƂC
2ƂFɂȂm߂ȂB

process
2ƂԂɂȂḿC\\
$\displaystyle \frac{{}_5 \rm{C} _2}{{}_8 \rm{C} _2}
=\displaystyle \frac{5 \times 4}{2 \times 1} \div \displaystyle \frac{8 \times 7}{2 \times 1}
=\displaystyle \frac{5}{14}$\\
2ƂɂȂḿC\\
$\displaystyle \frac{{}_3 \rm{C} _2}{{}_8 \rm{C} _2}
=\displaystyle \frac{3 \times 2}{2 \times 1} \div \displaystyle \frac{8 \times 7}{2 \times 1}
=\displaystyle \frac{3}{28}$\\
āC߂ḿC$\displaystyle\frac{13}{28}$\\
iʁj\\
2ƂԂɂȂḿC$\displaystyle\frac{5}{8}\times \displaystyle\frac{4}{7}=\displaystyle\frac{5}{14}$\\
2ƂɂȂḿC$\displaystyle\frac{3}{8}\times \displaystyle\frac{2}{7}=\displaystyle\frac{3}{28}$\\
āC$\displaystyle\frac{10+3}{28}=\displaystyle\frac{13}{28}$

$\displaystyle\frac{13}{28}$

6̐ԋʂ4̔ʂ̓Ă܂B
̒2̋ʂoƂC2ƂFłm߂B

process
10̒2oóC\\
$ {}_{10} \rm{C} _2 =\displaystyle \frac{10 \times 9}{2 \times 1} =45$ʂB\\
2Ƃԋʂoꍇ̐́C\\
$ {}_6 \rm{C} _2 =\displaystyle \frac{6 \times 5}{2 \times 1} =15$ʂB\\
2Ƃʂoꍇ̐́C\\
$ {}_4 \rm{C} _2 =\displaystyle \frac{4 \times 3}{2 \times 1} =6$ʂB\\
u2ƂԋʂoꍇvƁu2Ƃʂoꍇv͓ɂ͋NȂ̂ŁC
2ƂFɂȂꍇ̐$15+6=21$ʂB
āC߂m$\displaystyle \frac{21}{45}$

$\displaystyle \frac{21}{45}$

8̐ԋ12̔ʂ̓Ă܂B
̒1ʂoCoʂ܂ɂǂȂ̂ƂꍇC
1ڂɔʁC2ڂɐԋʂom߂B

process
20̋ʂ甒ʂom$\displaystyle \frac{12}{20}$B\\
c19̋ʂԋʂom$\displaystyle \frac{8}{19}$C\\
āC߂m
$\displaystyle \frac{12}{20} \times \displaystyle \frac{8}{19}=\displaystyle \frac{24}{95}$

$\displaystyle \frac{24}{95}$

5̍d݂𓯎ɓƂC\̏om̖ƂȂm߂B

process
5̍d݂̕\Ȅȏ$2^5=32$ʂB
̂\łꍇ̐lƁC\\
AF\0CȂ킿Sė̏ꍇ1ʂB\\
CF\2̏ꍇ$ {}_5 \rm{C} _2 =\displaystyle \frac{5 \times 4}{2 \times 1} =10$ʂB\\
EF\4̏ꍇ$ {}_5 \rm{C} _4 ={}_5 \rm{C} _1 =5$ʂB\\
v16ʂBċ߂ḿC
$\displaystyle \frac{16}{32}=\displaystyle \frac{1}{2}$

$\displaystyle \frac{1}{2}$

3̃TCR𓯎ɐUƂCoڂ̘̐a5ȉɂȂm߂B

process
3̃TCR̖$(aCbCc)$̏óC\\
$3^3=216$ʂB\\
5ȉ̏ꍇ́C\\
$(a, \, b, \, c)=\\
(1, \, 1, \, 1),(1, \, 1, \, 2),(1, \, 1, \, 3)\\
(1, \, 2, \, 1),(1, \, 2, \, 2),(1, \, 3, \, 1)\\
(2, \, 1, \, 1),(2, \, 1, \, 2),(2, \, 2, \, 1)\\
(3, \, 1, \, 1)$
̍v10ʂB\\
āC$\displaystyle \frac{10}{216}=\displaystyle \frac{5}{108}$

$\displaystyle \frac{5}{108}$

܂̒ɁCCԁC̋ꂼ20C25C30ĂB
2񑱂ċoƂC2ƂFom͂ǂꂩB
Co͌ɖ߂Ȃ̂ƂB

process
2Ƃ̊m$=\displaystyle \frac{20}{75} \times \displaystyle \frac{19}{74}=\displaystyle \frac{38}{555}$\\
2ƂԂ̊m$=\displaystyle \frac{20}{75} \times \displaystyle \frac{24}{74}=\displaystyle \frac{60}{555}$\\
2Ƃ̊m$=\displaystyle \frac{30}{75} \times \displaystyle \frac{29}{74}=\displaystyle \frac{87}{555}$\\
$\displaystyle \frac{38}{555}+\displaystyle \frac{60}{555}+\displaystyle \frac{87}{555}
=\displaystyle \frac{185}{555}=\displaystyle \frac{1}{3}$

$\displaystyle \frac{1}{3}$

̒15܂ł̐15̃J[hB
̔̒2̃J[hoƂC̘aɂȂm߂B

process
2̃J[h̎óC$ {}_5 \rm{C} _2 =10$ʂB̂aɂȂ̂́C\\
Ƌc(2,4)1ʂB\\
Ɗc1C3C52Iׂ΂悢C$ {}_3 \rm{C} _2 ={}_3 \rm{C} _1=3$ʂB\\
v4ʂB\\
āC ߂m$\displaystyle \frac{4}{10}=\displaystyle \frac{2}{5}$

$\displaystyle \frac{2}{5}$

1C2C3C44̃J[hB
̃J[h12񑱂ĎoCoɍEׂ֕2̐ƂC
̐23菬m߂B

process
SĂ̏ꍇ̐́C$ {}_4 \rm{P} _2 = 4 \times 3 =12$ʂB
23菬̂́C12C13C14C214ʂ肾C߂m
$\displaystyle \frac{4}{12}=\displaystyle \frac{1}{3}$B

$\displaystyle \frac{1}{3}$

܂̒ɐԋ5Ɣ3ĂB
̒2̋𓯎ɎoƂC1ԋC1łm߂B

process
SĂ̏ꍇ̐$ {}_8 \rm{C} _2 =\displaystyle \frac{8 \times 7 }{ 2 \times 1} =28$ʂB
1ԋC1łꍇ̐́C$5 \times 3=15$ʂB
āC߂ḿC$\displaystyle \frac{15}{28} $\\
iʁjԋC̏ɏom$\displaystyle \frac{5}{8} \times \displaystyle \frac{3}{7}$ł邪C
Cԋ̏ɏomȂ̂ŁC߂ḿC
$\displaystyle \frac{5}{8} \times \displaystyle \frac{3}{7} \times 2=\displaystyle \frac{15}{28}$

$\displaystyle \frac{15}{28} $






[Level7]

[Level8]

[EOF]
% t@C̍Ōɂ

{cȒP

TCR13om߂B

process
TCR̖ڂ̏o6ʂB̂3ô1ʂȂ̂ŁC߂m
$\displaystyle \frac{1}{6}$

$\displaystyle \frac{1}{6}$



