Question

How to solve questions like the following? "This exercise refers to a standard deck of playing cards. Assume that 8 cards are randomly chosen from the deck.How many hands contain exactly 3 queens?"

Answer 1

To solve the problem, use the combination formula to calculate the total number of possible hands and the number of ways to choose 3 queens.

Step-by-step explanation:

To solve the problem of finding the number of hands that contain exactly 3 queens, we need to consider the total number of possible hands and the number of ways we can choose 3 queens from the deck.

First, let's determine the total number of hands we can form by choosing 8 cards from a standard deck of 52 cards without replacement. This can be calculated using the combination formula, denoted as C(n, r), where n is the total number of items (52 cards) and r is the number of items chosen (8 cards). In this case, n = 52 and r = 8.

Next, we need to determine the number of ways we can choose 3 queens from a standard deck of 4 queens. This can be calculated using the combination formula as well, with n = 4 and r = 3.

Finally, we can find the number of hands containing exactly 3 queens by multiplying the total number of hands and the number of ways to choose 3 queens.