Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain no face cards?
A)639,730
B)319,865
C)127,946
D)658,008

Question

Quizplus · Accepted Answer

In a deck of 52 cards, there are 12 face cards (Jacks, Queens, Kings of each suit) and 40 non-face cards. To find the number of five-card hands with no face cards, we choose 5 cards out of the 40 non-face cards, which is calculated using the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, and k is the number of items to choose. So, C(40, 5) = 40! / [5!(40-5)!] = 658,008.

Of the 2,598,960 Different Five-Card Hands Possible from a Deck