# 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.