Six cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if exactly four cards are aces.
A)1,128
B)1,035
C)1,275
D)1,326
E)1,225

Question

Quizplus · Accepted Answer

There are 4 aces in a standard deck of 52 cards. So, the number of ways to choose 4 aces from 4 aces is 4C4 = 1. The number of ways to choose 2 cards from the remaining 48 cards is 48C2 = 1,128. Therefore, the total number of ways to choose 6 cards from a standard deck of playing cards if exactly four cards are aces is 1 * 1,128 = 1,128.

Six Cards Are Chosen at Random from a Standard Deck