From an ordinary deck of 52 playing cards,a two-card hand is dealt.In how many ways can the two cards be of the same face value?
A) 2
B) 6
C) 78
D) 104
E) 1326

Question

Quizplus · Accepted Answer

There are 13 different face values (Ace through King) in a deck of cards. For each face value, there are 4 cards, and we want to select 2 out of these 4. The number of ways to do this for one face value is $ \binom{4}{2} = 6 $. Since there are 13 different face values, the total number of ways is $ 13 \times 6 = 78 $.

From an Ordinary Deck of 52 Playing Cards,a Two-Card Hand