suit<-c("H","D","S","C")
number<-c("A","K","Q","J",10:2)

cards1<-suits1<-value1<-matrix(NA,4,13) 
for (i in 1:4) {
  for (j in 1:13) {
    cards1[i,j]<-paste(number[j],suit[i],sep="")
    suits1[i,j]<-suit[i]
    value1[i,j]<-number[j]
  }
}

cards<-as.vector(cards1)
suits<-as.vector(suits1)
values<-as.vector(value1)

deck<-data.frame(cards,values,suits)



draw<-sample(52,5,replace=FALSE)
hand<-deck[draw,]
hand


num.sims<-10000

full.house<-NULL
four.of.kind<-NULL
exactly.one.pair<-NULL
exactly.two.pairs<-NULL
exactly.three.of.kind<-NULL
zero.pairs<-NULL
for (i in 1:num.sims) {
  draw<-sample(52,5,replace=FALSE)
  hand<-deck[draw,]
  unique.vals<-unique(hand$values)
  full.house[i]<-ifelse(length(unique.vals)!=2,0,
                    ifelse(sum(hand$values==unique.vals[1])==2 |
                           sum(hand$values==unique.vals[1])==3, 1, 0))
  four.of.kind[i]<-ifelse(length(unique.vals)!=2,0,
                    ifelse(sum(hand$values==unique.vals[1])==1 |
                           sum(hand$values==unique.vals[1])==4, 1, 0))
  exactly.one.pair[i]<-ifelse(length(unique.vals)==4,1,0)
  exactly.two.pairs[i]<-ifelse(length(unique.vals)==3 & max(table(hand$values))==2,1,0)
  exactly.three.of.kind[i]<-ifelse(length(unique.vals)==3 & max(table(hand$values))==3,1,0)
  zero.pairs[i]<-ifelse(length(unique.vals)==5,1,0)
}


mean(full.house)   
13*12*choose(4,3)*choose(4,2)/choose(52,5)  # truth 

mean(four.of.kind)  
624/2598960   # truth

mean(exactly.one.pair)
13*choose(4,2)*choose(12,3)*4^3/choose(52,5)  # truth

mean(exactly.two.pairs)
(13*12*choose(4,2)*choose(4,2)*11*4/2)/choose(52,5)  # truth

mean(exactly.three.of.kind)
13*4*choose(12,2)*4^2/choose(52,5)  #truth

mean(zero.pairs)
(52*48*44*40*36/factorial(5))/choose(52,5)