Question

From a standard 52-card deck, how many 6 -card hands consist of 4 spades and 2 clubs? There are possible 6-card hands consisting of 4 spades and 2 clubs (Type a whole number.)

Answer 1

To find the number of 6-card hands that consist of 4 spades and 2 clubs, we calculate the number of ways to choose the spades and clubs separately and then multiply them together.

Step-by-step explanation:

To find the number of 6-card hands that consist of 4 spades and 2 clubs, we first need to determine how many ways we can choose 4 spades from the deck which has 13 spades. This can be calculated using the combination formula:

C(n, k) = n! / (k! * (n - k)!)

In this case, n = 13 and k = 4. So, the number of ways to choose 4 spades is: C(13, 4) = 13! / (4! * (13 - 4)!) = 715.

Next, we need to determine how many ways we can choose 2 clubs from the deck which has 13 clubs. Using the same formula, we get: C(13, 2) = 13! / (2! * (13 - 2)!) = 78.

Finally, to find the total number of 6-card hands that consist of 4 spades and 2 clubs, we multiply the number of ways to choose 4 spades by the number of ways to choose 2 clubs: 715 * 78 = 55,770.