You select 8 cards randomly from a deck of 52 cards.
What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)
12!(52-8)!/(52!)(12-8)!
check that. It should be
12/52 * 11/51* 10/50*9/49*....* 5!/45
To find the probability of selecting all face cards from a deck of 52 cards, we need to determine the number of favorable outcomes (the number of ways to select all face cards) and the total number of possible outcomes (the total number of ways to select 8 cards).
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.