### My code

n<-14

num.sims<-10000

all.diff.bday<-NULL
for(i in 1:num.sims) {
  b.days<-sample(365,n,replace=TRUE)
  all.diff.bday[i]<-length(unique(b.days))==n
}

mean(all.diff.bday)

factorial(n)*choose(365,n)/365^n    # equivalent to (365!/(365-n)!)/365^n


### Kelly's code

n=0
for(i in 1:10000){n=ifelse(length(unique(sample(1:365, 14, replace=TRUE)))==14, n+1, n+0)}
n/10000




### Nate's one-line code

mean((apply(matrix(sample(1:365,10000*14,replace=TRUE),ncol=14),1,anyDuplicated)==0)*1)