12!(52-8)!/(52!)(12-8)!
check that. It should be
12/52 * 11/51* 10/50*9/49*....* 5!/45
What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)
check that. It should be
12/52 * 11/51* 10/50*9/49*....* 5!/45
First, let's determine the number of ways to choose all face cards. In a deck of 52 cards, there are 12 face cards (4 jacks, 4 queens, and 4 kings). Since we are selecting 8 cards, we need to choose all 8 of these face cards. Therefore, the number of ways to select all face cards is:
C(12, 8) = 12! / (8! * (12 - 8)!) = 495
Next, let's determine the total number of ways to select 8 cards from a deck of 52 cards. This can be calculated using the combination formula:
C(52, 8) = 52! / (8! * (52 - 8)!) = 752,538,150
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 495 / 752,538,150
Therefore, the probability that all of the cards selected are face cards is 0.000000657 or approximately 6.57 x 10^-7.