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 choose any 5 cards.

To take at least 1 card of each suit, we first choose 4. There are 13*13*13*13 = 13^4 ways to choose 4 cards with different suits. Then there are 48 ways to choose the last card.

Thus,

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