A big box contains 14 pairs of shoes. If 9 shoes are randomly selected from the box, find the probability that there will be EXACTLY two complete pairs.

Question

Give the numerical value of this probability.

Answer 1

The denominator is straightforward: C(28,9) 2 pairs of 14 shoes is 2*14 = 28; choose 9

For the numerator, there are C(14,2) ways that you can choose the 2 pairs. Then, there are 5 additional shoes. There are C(12,5) ways to choose which pair the shoe is from, and 2^5 to choose the shoe from the pair.

C(14,2)C(12,5)2^5/C(24,9) = 2306304/6906900 = 192/575 = 0.333913043478261