Question

Poker game plays with a card deck of 52 cards (4 types and 13 numbers). 5 cards are given to each player. How many ways can you choose 5 cards from this deck?

Answer 1

There are 259,896 ways to choose 5 cards from a standard deck of 52 cards.

Step-by-step explanation:

In a standard deck of 52 cards, there are 4 suits (clubs, diamonds, hearts, spades) and 13 numbers (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) in each suit. To calculate the number of ways you can choose 5 cards from this deck, we use the concept of combinations.

The formula to calculate combinations is:

nCr = n! / (r!(n-r)!)

where n is the total number of items and r is the number of items being chosen.

In this case, n = 52 (total number of cards) and r = 5 (number of cards being chosen).

Substituting these values into the formula, we get:

nCr = 52! / (5!(52-5)!)

= 52! / (5!47!)

= (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)

Simplifying, we get:

nCr = 259,896

Therefore, there are 259,896 ways to choose 5 cards from a standard deck of 52 cards.