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: