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[Title]
301_ꍇ̐

% 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]
ibj
EԁE̐F1܂B
ɑIׂƂCʂ̕ו܂B

process
$3\, !=3 \times 2 \times 1=6$

6ʂ

EԁEE̐F1܂B
ɑIׂƂCʂ̕ו܂B

process
$4\, !=4 \times 3 \times 2 \times 1=24$

24ʂ

1C2C3C44̃J[hׂ4̐ƂCʂ̐ł邩B

process
$4 \, != 4 \times 3 \times 2 \times 1=24$ʂB

24ʂ

1C2C3C4C55̃J[hׂ5̐ƂCʂ̐ł邩B

process
$5 \, != 5 \times 4 \times 3 \times 2 \times 1=120$ʂB

120ʂ

[ACBCCCD4l鏇Ԃ͉ʂ肠邩B

process
$4 \, !=4 \times 3 \times 2 \times 1=24$

24ʂ

[ACBCCCDCE5l鏇Ԃ͉ʂ肠邩B

process
$5 \, !=5 \times 4 \times 3 \times 2 \times 1=120$

120ʂ

S̈قȂ鋳ȏɕׂ@͑Sŉʂ肠邩B

process
l͋ʂłB\\
$4 \, !=4 \times 3 \times 2 \times 1=24$ʂ

24ʂ

T̈قȂ鋳ȏɕׂ@͑Sŉʂ肠邩B

process
l͋ʂłB\\
$5 \, !=5\times 4 \times 3 \times 2 \times 1=120$ʂ

120ʂ

قȂT̖{Tl̎qǂɂPB̂ƂC{̂͑Sŉʂ肩B

process
$5 \, !=5\times 4 \times 3 \times 2 \times 1=120$ʂ

120ʂ

6l1ɕׂƂɁCו͉ʂ肠邩B

process
$6 \, != 6 \times 5 \times 4 \times 3 \times 2 \times 1=720$ʂB

720ʂ

7l1ɕׂƂɁCו͉ʂ肠邩B

process
$7 \, != 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1=5040$ʂB

5040ʂ

jqQlCqRl̍vTlɕԂƂC̕ѕ͑Sŉʂ肠邩B

process
l͋ʂłB\\
$5 \, !=5\times 4 \times 3 \times 2 \times 1=120$ʂ

120ʂ

jqRlCqSl̍vVlɕԂƂC̕ѕ͑Sŉʂ肠邩B

process
l͋ʂłB\\
$7 \, !=7\times 6\times 5\times 4 \times 3 \times 2 \times 1=5040$ʂ

5040ʂ

1C2C3C44̃J[h2ׂ2̐ƂCʂ̐ł邩B

process
$ {}_4 \rm{P} _2 =4 \times 3 =12$

12ʂ

1C2C3C44̃J[h3ׂ3̐ƂCʂ̐ł邩B

process
$ {}_4 \rm{P} _3 =4 \times 3 \times 2 =24$

24ʂ

2C3C4C5ƏꂽJ[h1܂B
3g3̐肽B
ʂ̐łł傤B

process
$ {}_4 \rm{P} _3 =4 \times 3 \times 2=24$

24ʂ

3C5C7C94̃J[hقȂ2oāC2̐ƂSŉʂł܂B

process
$ {}_4 \rm{P} _2 =4 \times 3 =12 $

12ʂ

P$\sim$T̐J[hꂼPBgĂłR̐́CSŉʂ肩B

process
$ {}_{5} \rm{P} _3 =5\times 4 \times 3 =60$

60ʂ

ɁCT̐F̈قȂB̂̂R̊EɕׂĐMƂCʂ̐Mł邩B

process
$ {}_{5} \rm{P} _3 =5 \times 4 \times 3 =60$

60ʂ

ACBCCCDCE5قȂ3Iŕׂו͉ʂ肠邩B

process
$ {}_5 \rm{P} _3 =5 \times 4 \times 3 =60$

60ʂ

eƎqǂSl̂UlƑB̉ƑsɍsāCLOʐ^Ƃ낤ƂĂBRlŎʐ^ƂƂC̕ѕ͉ʂ肩B

process
$ {}_{6} \rm{P} _3 =6\times 5 \times 4 =120$

120ʂ

VlCcCcCLePiC͂ȂjIԕ@͉ʂ肠邩B

process
${}_7 \rm{P} _3 =7\times 6 \times 5 =210ʂ$B\\

210ʂ

W̐1C2C3C4C5C6C7C8قȂRoĂłR͉̐邩B

process
${}_8 \rm{P} _3 =8 \times 7\times 6 =336ʂ$B\\

336ʂ

10̍i̒3iIŁCȊwb܁Csm܁Cψ܂ɂƂC
̌ߕ͉ʂ肠邩B

process
$ {}_{10} \rm{P} _3 =10 \times 9 \times 8 =720$

720ʂ

PNX40l̒CcCcCL̍vRlIтB̑Iѕ͑Sŉʂ肩B

process
$ {}_{40} \rm{P} _3 =40\times 39 \times 38 =59280$

59280ʂ

jqSlCqRlPɕԂƂCjqƏq݂ɕԕѕ͉ʂ肠邩B

process
jqMCqWŕ\ƁCjqƏq̈ʒúuMWMWMWMWv̂PʂłB\\
$4 \, !\times 3\, != (4 \times 3 \times 2 \times 1)\times(3 \times 2 \times 1)=144$ʂB

144ʂ

0C2C4̃J[h3͉̐ʂł܂B

process
3ڂ2܂4B2ڂ1ڂ́Cc2ׂ̐΂悢C\\
$2 \times 2\,!=2 \times 2 \times 1=4ʂ$

4ʂ

0C1C2C3̃J[h4͉̐ʂł܂B

process
4ڂ1܂2܂3B3ڂ2ڂ1ڂ́Cc3ׂ̐΂悢C\\
$3 \times 3\,!=3 \times 3 \times 2 \times 1=18ʂ$

18ʂ






[Level2]
~Cdg
6l~`̃e[uɒȂƂC͉ʂ肠邩B

process
1lŒ肷ƁCc5lׂ΂悢B
$(6-1)\,!=5\,!=120$ʂ

120ʂ

F̈Ⴄ4̋ʂCACBCCƋLꂽ̂ꂩɓƂC
󂫔Ă悢ƂāC͉ʂ肠邩B

process
4̋ʂuCCCvƂB
̂ꂼ̋ʂɑ΂āCACBCC3ʂ̓̂ŁC
$3^4=81$ʂ

81ʂ








[Level3]
iZbj
1C3C5C74̃J[h1xg4̐ƂC5̔{͑Sŉʂ肠܂B

process
1ڂ5̂ƂCc̐1C3C74ځC3ځC2ڂɕׂ΂悢C\\
$ {}_3 \rm{P} _3 =3 \times 2 \times 1 =6 $

6ʂ

1C2C3C4C5̒̈قȂ3̐gĂł3͉̋邩B

process
1̈ʂ́C2C4̂ǂ炩2ʂB
̕S̈ʂƏ\̈ʂɂ͏͂Ȃ̂ŁC$ {}_4 \rm{P} _2$ʂB
āC
$2 \times {}_4 \rm{P} _2 =2 \times 4 \times 3 =24$

24ʂ

jq3lCq3l1ɕׂƂC[jqł悤ȕו͉ʂ肠邩B

process
3l̒jq2lIŗ[ɕׂו́C
${}_3 \rm{P} _2 =3 \times 2 =6ʂ$B\\
Ɏc4l̕ו́C\\
${}_4 \rm{P} _4 =4 \times 3 \times 2 \times 1=24ʂ$B\\
āC߂ו
$6 \times 24=144$ʂ

144ʂ

jq4lCq3l1ɕׂƂC3l̏qׂ荇悤ȕѕ͉ʂ肠܂B

process
q3l̕ו
${}_3 \rm{P} _3 =3 \times 2 \times 1=6ʂ$B\\
3l̏q̃Zbgƒjq4ľv5l̕ו\\
${}_5 \rm{P} _5 =5 \times 4 \times 3 \times 2 \times 1=120ʂ$B\\
āC߂ו́C$6 \times 120=720$ʂ

720ʂ

jqRlCqQl1ɕׂƂCQl̏qׂ荇悤ȕѕ͉ʂ肠܂B

process
qQl̕ו
$2\,! = 2 \times 1=2ʂ$B\\
̂Ql̏q̃ZbgƒjqRľvSl̕ו\\
$4\,!=4\times 3\times 2\times 1 =24ʂ$B\\
āC߂ו́C$2 \times 24=48$ʂ

48ʂ

jqSlCqQl1ɕׂƂCQl̏qׂ荇悤ȕѕ͉ʂ肠܂B

process
qQl̕ו
$2\,! = 2 \times 1=2ʂ$B\\
̂Ql̏q̃ZbgƒjqSľvTl̕ו\\
$5\,!=5\times 4\times 3\times 2\times 1 =120ʂ$B\\
āC߂ו́C$2 \times 120=240$ʂ

240ʂ

ɁCACBCCCDCÊTl̐lB̒Ql̐lɕԕ@́CSŉʂ肠邩B

process
$ {}_{5} \rm{P} _2 =5\times 4 =20$

20ʂ

400m[̓o^͕⌇܂߂ĂTlłB̒烌\̃o[Sl鏇܂߂Č߂@͉ʂ肠邩B

process
$ {}_{5} \rm{P} _4 =5\times 4 \times 3 \times 2 =120$

120ʂ

jqTlCqSlɕԂƂC[qłѕ͉ʂ肠邩B

process
Sl̏q2lIŗ[ɕׂו́C
${}_4 \rm{P} _2 =4 \times 3 =12ʂ$B\\
ɎĉVl̕ו́C\\
$7 \, != 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1=5040$ʂB\\
āC߂ו
$12 \times 5040=60480$ʂ

60480ʂ

jqTlCqSlɕԂƂCqSl܂Ƃ܂ĕԕѕ͉ʂ肠邩B

process
qSl̕ו́C\\
$4 \, != 4 \times 3 \times 2 \times 1=24$ʂB\\
̂ꂼɑ΂āCjqTlƏqЂƂ܂̕ו\\
$6 \, != 6 \times 5 \times 4 \times 3 \times 2 \times 1=720$ʂB\\
āC$24\times 720=17280$ʂ

17280ʂ

eƎqǂRlB̂TlɕԂƂCe[ɂו͉ʂ肠邩B

process
e𗼒[ɕׂו́C
$2 \, != 2\times 1 =2ʂ$B\\
̂ꂼɑ΂āCqǂRl̕ו\\
$3 \, !=3 \times 2 \times 1=6$ʂB\\
āC߂ו
$2 \times 6=12$ʂ

12ʂ

eƎqǂRlB̂TlɕԂƂCeׂ荇ו͉ʂ肠邩B

process
e𗼒[ɕׂו́C
$2 \, != 2\times 1 =2ʂ$B\\
̂ꂼɑ΂āCqǂRlƗeЂƂ܂̕ו\\
$4 \, !=4\times  3 \times 2 \times 1=24$ʂB\\
āC߂ו
$2 \times 24=48$ʂ

48ʂ

jqSlCqRlɕԂƂCqRlKׂ荇ĕԂƂ̕ו͉ʂ肠邩B

process
qRl̕ו́C
$3\, !=3\times 2\times 1 =6ʂ$B\\
̂ꂼɑ΂āCjqSlƏqЂƂ܂̕ו\\
$5 \, !=5\times 4\times  3 \times 2 \times 1=120$ʂB\\
āC߂ו
$6 \times 120=720$ʂ

720ʂ

jqSlCqRlɕԂƂCj݂ɕԂƂ̕ו͉ʂ肠邩B

process
jqMCqWŕ\ƁCj̈ʒúuMWMWMWMv̈ʂłB
āC߂ו
$4\,!\times 3\,!=(4\times 3\times 2\times 1)\times (3\times 2\times 1)=144$ʂ

144ʂ

jqRlCqRlɕԂƂCj݂ɕԕѕ͉ʂ肠邩B

process
jqMCqWŕ\ƁCӂ̒j̈ʒu\\
uMWMWMWvƁuWMWMWMv̂QʂB
āC߂ו́C\\
$3\,! \times 3\,! \times 2=72$ʂ

72ʂ

jqSlCqSlɕԂƂCj݂ɕԕѕ͉ʂ肠邩B

process
jqMCqWŕ\ƁCӂ̒j̈ʒu\\
uMWMWMWMWvƁuWMWMWMWMv̂QʂB
āC߂ו́C\\
$4\,! \times 4\,! \times 2=1152$ʂ

1152ʂ

1C2C3C4C5̂T̐gāCR̐ƂC͉ʂ肠邩BCP̐͂P񂵂gȂ̂ƂB

process
P̈ʂ́u2܂4v̂QʂB̂ꂼɑ΂āCĉS̐QIѕSC\̈ʒuɕׂ΂悢${}_4 \rm{P} _2 =4 \times 3 =12ʂ$BāC
$2\times 12=24$ʂ

24ʂ

1C2C3C4C5̂T̐gāCR̐ƂCT̔{͉ʂ肠邩BCP̐͂P񂵂gȂ̂ƂB

process
P̈ʂ́uTv̂PʂB̂Pʂɑ΂āCĉS̐QIѕSC\̈ʒuɕׂ΂悢${}_4 \rm{P} _2 =4 \times 3 =12ʂ$BāC
$1\times 12=12$ʂ

12ʂ

T̕$a$C$b$C$c$C$d$C$e$ɕׂƂC$a$C$b$[ɂ悤ȕו͉ʂ肠邩B

process
ij$a \bigcirc\bigcirc\bigcirc b$\\
$a$C$b$̕ו$2\,!$ʂBԂ̕̕ו$3\,!$ʂB\\
$2\,!\times 3\,!=(2\times 1)\times (3\times 2\times 1)=12$ʂ

12ʂ

j3lC4l킹7l1ɕׂāC
[jłꍇ̕ו͉ʂ肠邩B

process
3l̒jq2lIŗ[ɕׂו́C
${}_3 \rm{P} _2 =3 \times 2 =6ʂ$B\\
Ɏc5l̕ו́C\\
${}_5 \rm{P} _5 =5 \times 4 \times 3 \times 2 \times 1=120ʂ$B\\
āC߂ו
$6 \times 120=720$ʂ

720ʂ

15܂ł5̃J[hSgč5̐̂C
35ׂ荇͉̂邩B

process
35̕ו2ʂB
35Zbg1ƂāC4̃J[h̕ו$4\,!=24$ʂB
āC$2\times 4\,!=2\times 24=48$

48

1C2C3C44̃J[hׂ4̐ƂC4000ȏ͉̐ʂł邩B

process
4ڂ4͌Œ肵ĂāCc1C2C33̃J[hׂ΂悢C\\
$ 3 \, !=3 \times 2 \times 1 =6$

6ʂ

0C1C2C3C45̃J[h3̐ƂC320͏牽ԖڂB

process
3ڂ1̂ƂC2ځC1ڂ͎c4̐2Iŕׂ΂悢C
$ {}_4 \rm{P} _2 =4 \times 3 =12$ʂB
3ڂ2̂Ƃlɂ$ {}_4 \rm{P} _2 =4 \times 3 =12$ʂB
3ڂ3̂Ƃ͏301C302C304C310C312C314C320ƕԂC\\
$12+12+7=31$ԖځB

31Ԗ

1C2C3C44̃J[h2ׂ2̐ƂC3̔{͉ʂł邩B

process
3̔{́ue̘̐aR̔{vC\\
12C21C24C424ʂB

4ʂ

1C2C3C44̃J[hB
4̃J[h1ɕׂ4̐ƂC
3100傫ɂȂו͑Sŉʂ肠邩B

process
4ڂ3̂ƂCc̃J[h1C2C4ׂ΂悢C$3 \, !=3 \times 2 \times 1=6$ʂB\\
4ڂ4̂ƂCc̃J[h1C2C3ׂ΂悢C$3 \, !=3 \times 2 \times 1=6$ʂB\\
v12ʂ

12ʂ

0`3܂ł̐J[h1B4̃J[hg4̐ƂC
2100傫ɂȂו͑Sŉʂ肠邩B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic13.tex}
\end{center}

10ʂ

0C1C2C3C4C5̒̈قȂ3̐g3̐ƂC5̔{͉ł邩B

process
̈ʂ0̂ƂCS̈ʂƏ\̈ʂɂ15܂ł52Iŕׂ΂悢̂ŁC
$ {}_5 \rm{P} _2=5 \times 4=20$ʂB\\
̈ʂ5̂ƂCS̈ʂ1C2C3C44ʂB
ɁCႦΕS̈ʂ1Ȃ΁C\̈ʂ͎c0C2C3C44ʂB
āC$4 \times 4=16$ʂB\\
āC߂35̔{́C$20+16=36$B

36

0C1C2C3C4C5قȂ4̐IłƂC4͉̋ł邩B

process
̈ʂ0̂ƂCCSC\̈ʂɂ15܂ł53Iŕׂ΂悢̂ŁC
$ {}_5 \rm{P} _3=5 \times 4 \times 3=60$ʂB\\
̈ʂ2̂ƂC̈ʂ1C3C4C54ʂB
ɁCႦΐ̈ʂ1Ȃ΁CSC\̈ʂ͎c0C3C4C52Iŕׂ΂悢̂ŁC
$4 \times 3 =12$ʂBāC$4 \times 12=48$ʂB\\
̈ʂ4̂ƂClɂ48ʂB
āC߂ꍇ̐́C$60+48+48=156$B

156

1C2C3C4C5C6قȂ4̐I4̐B
2300ȏ̐͂ł邩B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic14.tex}
\end{center}
̈ʂ̐3ȏ̂Ƃ͕K2300ȏɂȂ̂ŁC\\
$4 \times 5 \times 4 \times 3=240$B\\
̈ʂ̐2̂Ƃ͕S̈ʂ3ȏȂ2300ȏɂȂ̂ŁC\\
$1 \times 4 \times 4 \times 3=48$B\\
āC߂鑍́C$240+48=288$B

288

jqSlCqRlɕԂƂCqׂ荇Ȃ悤ɕԂƂ̕ו͉ʂ肠邩B

process
jqMCq邷Ԃ$|$ŕ\ƁCu${\rm |\,M\,|\,M\,|\,M\,|\,M\,|}$vB
jqSlׂĂCԂTRIяqׂ΂悢B
āC߂ו\\
$4\,!\times {}_5 \rm{P} _3 =(4\times 3\times 2\times 1)\times (5\times 4\times 3)=24\times 60=1440$ʂ

1440ʂ

1C2C3C4C5̂T̐gāCR̐ƂC[̐ł͉̂ʂ肠邩BCP̐͂P񂵂gȂ̂ƂB

process
uv̈ʒuɐׂ΂悢B
u1C3C5v̂R̐QIŁuv̈ʒuɕׁCĉR̐PIсuv̈ʒuɒu΂悢C
${}_3 \rm{P} _2 \times {}_3 \rm{P} _1=(3 \times 2\times 1)\times 3 =18ʂ$B

18ʂ

5̐1C2C3C4C5ׂ̂ĂgĂł5̊͂邩B

process
1ڂɁu1C3C5v1IԁB
ɁCႦ1ڂɁu1vgꍇCću2C3C4C5v2$\sim$5ڂɕׂ΂悢B\\
$3\times 4 !=3\times 24=72$

72

ACBCC3lł񂯂ƂCɂȂꍇ͉ʂ肠邩߂ȂB

process
ACBCCuO[CO[CO[vȂǂƓꍇ3ʂB
ACBCCuO[C`LCp[vȂǂƑSĈقȂꍇ$3!=6$ʂB
v9ʂ

9ʂ

jq4lCq2l1ɕׂƂCq2lׂ荇Ȃו͉ʂ肠邩B

process
$| \bigcirc | \bigcirc | \bigcirc | \bigcirc |$\\
jq4lׂĂC52Iŏq2lׂ΂悢C\\
$4\,! \times {}_5 \mathrm{P}_2=12\times 40=480$

480ʂ






[Level4]
gibj
̔@ŊʃW[X𔃂ɂ܂B
ɂ́CO[vt[cCIWCAbvCuhEC}XJbgC}S6ނ̈ݕB
NN͂̒2ނIԁBʂ̑Iѕ邩B

process
$ {}_6 \rm{C} _2 =\displaystyle \frac{6 \times 5}{2 \times 1} =15$ʂB

15ʂ

̔@ŊʃW[X𔃂ɂ܂B
ɂ́CO[vt[cCIWCAbvCuhEC}XJbgC}S6ނ̈ݕ܂B
䂤q́C̒3ނ𔃂ƎvĂ܂B
ݕ̑Iѕ͉ʂ肠܂B

process
$ {}_6 \rm{C} _3 =\displaystyle \frac{6 \times 5 \times 4}{3 \times 2 \times 1} =20$ʂB

20ʂ

~ɃACCCECGCI5̓_B𒸓_ƂOp`͂邩B

process
$ {}_5 \rm{C} _3 =\displaystyle \frac{5 \times 4 \times 3}{3 \times 2 \times 1} =10$ʂB

10ʂ

jq3lCq5lB
|Ԃ3lIԂƂƁCʂ̕@܂B

process
lԂ͋ʂł邩C\\
$ {}_8 \rm{C} _3 =\displaystyle \frac{8 \times 7 \times 6}{3 \times 2 \times 1} =56$ʂB

56ʂ

قȂ5̂ACBCCCDCE3Ƃg͉ʂ肠邩B

process
$ {}_5 \rm{C} _3 =\displaystyle \frac{5 \times 4 \times 3}{3 \times 2 \times 1} =10$ʂB

10ʂ

5l̒jq6l̏q̒3lIԂƂCjqq܂܂g͉gł邩B

process
jq2lCq1lƂȂg̐́C\\
$ {}_5 \rm{C} _2 \times {}_6 \rm{C} _1=\displaystyle \frac{5 \times 4}{2 \times 1} \times 6=60$ʂB\\
jq1lCq2lƂȂg̐́C\\
$ {}_5 \rm{C} _1 \times {}_6 \rm{C} _2=5 \times \displaystyle \frac{6 \times 5}{2 \times 1} =75$ʂB\\
āC$60+75=135$g\\
iʉj
ujqq܂܂v̔΂́CuׂĒjqv܂́uׂďqvł邩C\\
$ {}_{11} \rm{C} _3-\left({}_5 \rm{C} _3 +{}_6 \rm{C} _3\right)=165-(10+20)=135$g

135g

jq5lCq4l̒4l̈ψIԂƂC
qȂƂ1lĂIѕ͉ʂ肩B

process
uq1lȏv̔΂́uq0lvCȂ킿uׂĒjqvł邩C\\
$ {}_9 \rm{C} _4-{}_5 \rm{C} _4=
\displaystyle\frac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}
-\displaystyle\frac{5\times 4\times 3\times 2}{4\times 3\times 2\times 1}=121$

121ʂ

}̂悤5{̕sƑ3{̕sĂ܂B
̒ɂĂ̕slӌ`ł邩B
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic15.tex}
\end{center}

process
$ {}_5 \rm{C} _2\times {}_3 \rm{C} _2=
\displaystyle\frac{5\times 4\times 3}{3\times 2\times 1}
\times \displaystyle\frac{3\times 2 \times 1}{3\times 2\times 1}=10\times 3=30$

30

}ɂāCABɎŒZ͉ʂ肠邩B
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic16.tex}
\end{center}

process
ij^^^^\\
$ {}_8 \rm{C} _4 =\displaystyle \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} =70$ʂB

70ʂ

}ɂāCABɎŒZ͉ʂ肠邩B
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic17.tex}
\end{center}

process
ij^^^^\\
$ {}_4 \rm{C} _2 \times {}_4 \rm{C} _2
=\displaystyle \frac{4 \times 3 }{2 \times 1}\times \displaystyle \frac{4 \times 3 }{2 \times 1} =36$ʂB

36ʂ

jq6lCq5l̒C
jq2lCq2lIԂƂCIѕ͉ʂ肠邩B

process
$ {}_6 \rm{C} _2 \times {}_5 \rm{C} _2 
=\displaystyle \frac{6 \times 5}{2 \times 1} \times  \displaystyle \frac{5 \times 4}{2 \times 1} =150$ʂB

150ʂ








[Level5]
gibj
2Cԋ1C3̒C3̋ʂIяoꍇ͉̐ʂ肠邩B

process
WCԂRCBŕ\B\\
(W, R ,B)=\\
\  (2,1,0),(0.1,2),\\
\  (1,0,2),(2,0,1),\\
\  (0,0,2),(1,1,1)

v6ʂ

140܂ł̐̒C1̐IԂƂCꂪ5܂13̔{ł̂́C
Sŉʂ肠܂B

process
5̔{$40 \div 5=8]0$C8ʂB\\
13̔{$40 \div 13=3]1$C3ʂB\\
513̔{CȂ킿78̔{0B\\
āC߂̂́C\\
$8+3=11ʂ$

11ʂ

10~450~ʁC100~ʂgݍ킹590~ɂ̂ɂ͉ʂ肠܂B
C50~ʁC100~ʂ͂ꂼꏭȂƂ1͗p̂ƂB

process
50~ʁC100~ʂgݍ킹550~ɂꍇ̐l΂悢B\\
$i50~ʁC100~ʁj=\\$
$(1,5),(3,4),(5,3),(7,2),(9,1)$Bv5ʂ

5ʂ

19܂ł̐قȂ2̐IԂƂC
2̘̐aɂȂꍇ͉ʂ肩B

process
aɂȂ̂́C2̐umv܂́umv̂ƂB
āC
1C3C5C7C92IԂC2C4C6C82Iׂ΂悢B\\
$ {}_5 \rm{C} _2+ {}_4 \rm{C} _2
=\displaystyle\frac{5 \times 4}{2\times 1}\times \displaystyle\frac{4 \times 3}{2\times 1}=16$

16ʂ

}ɂāCABɎŒZ͉ʂ肠邩B
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic18.tex}
\end{center}

process
ׂĂ̌oH́C
$ {}_6 \rm{C} _3 =\displaystyle \frac{6 \times 5 \times 4 }{3 \times 2 \times 1}=20$ʂB
܂C~̏ʂoH́C\\
$ {}_3 \rm{C} _2 \times 1\times {}_2 \rm{C} _1= 3\times 1 \times 2=6$ʂB\\
āC߂oH́C$20-6=14$ʂ

14ʂ

}ɂāCABɎŒZ͉ʂ肠邩B
C2̒n_PCQ͕KʂƂB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic19.tex}
\end{center}

process
$ {}_4 \rm{C} _2 \times {}_3 \rm{C} _2 \times {}_4 \rm{C} _2 =6 \times 3 \times 6=108$ʂB

108ʂ

}ɂāCABɎŒZ͉ʂ肠邩B
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic20.tex}
\end{center}

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/301_ꍇ̐/pic20p.tex}
\end{center}
ׂĂ̌oH̐_PʂoH̐΂悢B\\
$ {}_{10} \rm{C} _5 - {}_5 \rm{C} _2 \times {}_5 \rm{C} _2=252-100=152$ʂ

152ʂ

9l̐k3l3gɕ@͉ʂ肠邩B

process
9l̐k3lACBCC̑gɕ@
${}_9 \mathrm{C}_3 \times {}_6 \mathrm{C}_3$łB
ACBCC̕ו$3\,!$ł邩C\\
$\displaystyle\frac{{}_9 \mathrm{C}_3 \times {}_6 \mathrm{C}_3}{3\,!}=280$ʂ

280ʂ




[Level6]
񐔂̐
144̖̐񐔂͑Sł邩B

process
$144=2^4 \cdot 3^2$\\
āC144̖񐔂́C\\
$2^x \cdot 3^y\,(0\leqq x \leqq 4,\,0\leqq y \leqq 2)$\\
ŕ\̂ŁC\\
$(4+1)\times (2+1)=15$ʂ

15ʂ

200̖̐񐔂͑Sł邩B

process
$200=2^3 \cdot 5^2$\\
āC200̖񐔂́C\\
$2^x \cdot 3^y\,(0\leqq x \leqq 3,\,0\leqq y \leqq 2)$\\
ŕ\̂ŁC\\
$(3+1)\times (2+1)=12$ʂ

12ʂ

144̖̐񐔂̑a͂B

process
$144=2^4 \cdot 3^2$\\
āC144̖񐔂́C\\
$2^x \cdot 3^y\,(0\leqq x \leqq 4,\,0\leqq y \leqq 2)$\\
ŕ\̂ŁC\\
$(2^0+2^1+2^2+2^3+2^4)\times(3^0+3^1+3^2)=31\times 13=403$

403






[Level7]



[EOF]
