Question

You were given a standard deck of 52 cards. You are dealt four cards face-down and one card face-up. The face-up card is the ace of clubs. Given this partial information, how many different five-card hands could you have been dealt such that you now have four cards of the same rank?

a) 48
b) 12
c) 11
d) 13

Answer 1

With the ace of clubs shown, there are 48 different hands that can produce a four-of-a-kind in aces, as the fifth card can be any of the remaining 48 cards in the deck.

Step-by-step explanation:

You have been dealt the ace of clubs and need to determine how many different five-card hands could be possible if the remaining four cards are also aces to have a four-of-a-kind. Since you already have one ace, there are only three aces left in the deck. These three must be included in your hand (ace of diamonds, ace of hearts, and ace of spades). The fifth card can be any of the remaining 48 cards in the deck that are not aces. Therefore, there are 48 different hands that satisfy the condition of having four cards of the same rank when one card is the ace of clubs.