98.7k views
0 votes
A poker hand consists of 5 cards from a standard deck of 52. How many hands will include all red cards or all black cards?

User Shamese
by
7.9k points

1 Answer

3 votes

Answer:There are two cases to consider: a hand that consists of all red cards and a hand that consists of all black cards.

Case 1: All red cards

There are 26 red cards in a standard deck of 52 cards. To form a 5-card hand consisting of all red cards, we need to choose 5 cards from the 26 red cards. The number of ways to do this is:

C(26, 5) = (26!)/(5!21!) = 65,780

Case 2: All black cards

Similar to the first case, there are 26 black cards in a standard deck of 52 cards. To form a 5-card hand consisting of all black cards, we need to choose 5 cards from the 26 black cards. The number of ways to do this is:

C(26, 5) = (26!)/(5!21!) = 65,780

Therefore, the total number of hands that include all red cards or all black cards is the sum of the two cases:

65,780 + 65,780 = 131,560

So there are 131,560 hands that consist of either all red cards or all black cards.

Explanation:

User Esin
by
8.2k points