Question

In how many ways can 9 hearts be chosen if 12 cards are chosen from a well-shuffled deck of 52 playing cards? a) 715 b) 220 c) 108 d) 6,534,385 e) 117 f) None of the above.

Answer 1

Answer: d) 6,534,385

Therefore, the number of ways of selecting 9 hearts is 6,534,385

Explanation:

Given;

Number of cards to be chosen = 12

Number of hearts to be chosen = 9

Number of non-hearts to be selected = 3

Total number of cards = 52

Number of hearts total = 13

Number of non-hearts total= 39

The number of ways of selecting hearts can be given by the illustration below.

Number of ways of selecting hearts × number of ways of selecting non-hearts

N = 13C9 × 39C3 (it's combination since order is not important)

N = 13!/(9! ×4!) × 39!/(36! × 3!)

N = 6,534,385

Therefore, the number of ways of selecting 9 hearts is 6,534,385