Originally Posted by

**p0oint** Hello!

I got one problem.

It says:

Out of deck of 52 cards we choose 20 cards and we return each card back into the deck. Count the probability that there will be 5 cards of clubs, diamonds, hearts, spades.

A - 5 cards of clubs

B- 5 cards of diamonds

C- 5 cards of hearts

D- 5 cards of spades

let N be the number of ways of getting 5 cards out of 13.

combinations with repetition:

N(A)=Binomial(13+5-1,5) = Binomial(17,5)=N(B)=N(C)=N(D)

Now I do this:

Assuming the experiments are independent (because we return the card in the deck):

I have probability P = Binomial(17,5) ^4 / Binomial(71,20)

These are combinations with repetition.

I get P = 0.0065059

But I tried the experiment with R Commander and it gives me P = 0.010666 with about 1 000 000 times throwing 20 cards.

So what is correct?

Thanks in advance.