Question

4. You are playing poker with some friends and are about to be delt 5 cards from a

well - shuffled deck.
A) How many different hands are possible?
B) How many hands contain clubs?

Answer 1

There are 2,598,960 possible 5-card hands in poker when dealt from a well-shuffled 52-card deck, and 1,287 of these hands can be made up entirely of clubs.

Step-by-step explanation:

Calculating Different Poker Hands

To calculate the number of different possible hands in poker when dealt 5 cards from a well-shuffled 52-card deck, we use combinations as the order of the cards does not matter.

The formula for combinations is C(n, k) = n! / (k! (n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial.

For the total number of different 5-card hands (part A), n is 52 and k is 5:

C(52, 5) = 52! / (5!(52-5)!) = 2,598,960 possible hands.

For the number of hands containing only clubs (part B), since there are 13 clubs, and we want all 5 cards to be clubs:

C(13, 5) = 13! / (5!(13-5)!) = 1,287 possible hands.