Suppose we pick 5 cards out of a deck of 52 What is the prob

Suppose we pick 5 cards out of a deck of 52. What is the probability that we get at least one card of each suit?

Solution

There are 52C5 ways to get any 5 cards.

Getting one of each suit first, there are 13^4 ways to do that. Then we are free to choose the 5th one, in 48 ways.

Thus,

P(at least one of each suit) = [13^4 * 48] / (52C5) = 0.527490996 [answer]