# How many 13 card hands having exactly 11 diamonds can be dealt?

## How many 13 card hands having exactly 11 diamonds can be dealt?

To get the probability of being dealt a 13-card hand with 11 diamonds, we just need to divide this number by the total number of 13-card hands. This is , about billion 13-card hands. So the probability is . This is about 1 in 10 million.

How many 5 card hands can a deck of 52 cards make?

Probability of Three of a Kind First, count the number of five-card hands that can be dealt from a standard deck of 52 cards. We did this previously, and found that there are 2,598,960 distinct poker hands.

### How many ways are there to distribute a deck of 52 cards to 4 players?

There are four possible recipients for each of the 52 cards, so there are 452 ways to distribute the cards to four people without restriction.

How many different 13 card bridge hands are there that contain all four aces?

(e) How many different 13-card bridge hands contain all four aces? Such a hand is determined by its 13 – 4 = 9 non-ace cards, which can be any of the 48 non-ace cards in the deck. Thus, there are ( 48 9 ) such hands.