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ๅ้ก
ๅ็ญ
1ๅๅกใใจใใ็ฝใใน8ๅใฎๅๅพใจ้่จ9ใๆใซใ้ปใในใ1ๅๅ
ฅใใใฐใใใ
$$\binom{9}{1}=9$$
2ๅๅกใใจใใ็ฝใใน7ๅใฎๅๅพใจ้่จ8ใๆใซใ้ปใในใ2ๅๅ
ฅใใใฐใใใ
$$\binom{8}{2}=28$$
kๅๅกใใจใใ็ฝใใน9-kๅใฎๅๅพใจ้่จ9-k+1ใๆใซใ้ปใในใkๅๅ
ฅใใใฐใใใ
$$\binom{10-k}{k}$$
| ้ปใใน | ็ฝใใน | ้ใๆฐ |
|---|---|---|
| 1 | 8 | 9 |
| 2 | 7 | 28 |
| 3 | 6 | 35 |
| 4 | 5 | 15 |
| 5 | 4 | 1 |
| Total | 88 |
Rใงๆค่จผใใฆใฟใใ
> event.all <- expand.grid( c(0,1), c(0,1), c(0,1), c(0,1), c(0,1), c(0,1), c(0,1), c(0,1), c(0,1) )
> # ็ฝใ้ปใใ็ฝใฏ0ใ้ปใฏ1
> exam <- matrix( 0, nrow(event.all), ncol(event.all)-1 )
> for ( i in 1:(ncol(event.all)-1) ) {
+ exam[,i] <- event.all[,i] * event.all[,i+1]
+ }
> # ้ฃใฎๅใจๆใ็ฎใใใใ้ปใในใ้ฃ็ถๅบใๅ ดๅใ็ฉใ1ใจใชใใ้ฃ็ถใงใชใๅ ดๅใ็ฉใ0ใจใชใใ
> sum( apply(exam, 1, sum) == 0 ) - 1
[1] 88
> # ็ฉใฎๅใ0ใงใใใฐใ้ฃ็ถใซๅกใใใฆใใชใใๅคใ0ใงใใๆฐkใฏๅ
จ้ใใฎๆฐใงใใใๅฐใชใใจใ1ใคใฎ้ปใในใๅกใใฎใงใk-1ใฏ็ญใใจใชใใ
ใณใผใ
code.r
event.all<-expand.grid(c(0,1),c(0,1),c(0,1),c(0,1),c(0,1),c(0,1),c(0,1),c(0,1),c(0,1))# ็ฝใ้ปใใ็ฝใฏ0ใ้ปใฏ1exam<-matrix(0,nrow(event.all),ncol(event.all)-1)for(iin1:(ncol(event.all)-1)){exam[,i]<-event.all[,i]*event.all[,i+1]}# ้ฃใฎๅใจๆใ็ฎใใใใ้ปใในใ้ฃ็ถๅบใๅ ดๅใ็ฉใ1ใจใชใใ้ฃ็ถใงใชใๅ ดๅใ็ฉใ0ใจใชใใsum(apply(exam,1,sum)==0)-1# ็ฉใฎๅใ0ใงใใใฐใ้ฃ็ถใซๅกใใใฆใใชใใๅคใ0ใงใใๆฐkใฏๅ
จ้ใใฎๆฐใงใใใๅฐใชใใจใ1ใคใฎ้ปใในใๅกใใฎใงใk-1ใฏ็ญใใจใชใใRegister as a new user and use Qiita more conveniently
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