Question

In a standard 52-card deck, how many different unordered pairs of two cards sum to 15?

a) 4
b) 8
c) 12
d) 16

Answer 1

In a standard 52-card deck, there are 58 different unordered pairs of two cards that sum to 15.

Step-by-step explanation:

In a standard 52-card deck, there are 4 suits with 13 cards each. To find the number of different unordered pairs that sum to 15, we need to count the number of pairs that consist of a number card (2-10) and a face card (J, Q, K) or two number cards that add up to 15.

There are 4 face cards in each suit, so the number of pairs with a number card and a face card is 4*13 = 52.

The number of pairs with two number cards that add up to 15 is 6, which can be obtained by counting the pairs (6,9), (7,8), (8,7), (9,6), (7,8), and (8,7).

Therefore, the total number of different unordered pairs of two cards that sum to 15 is 52 + 6 = 58.