September 2012
Problem of the Month

Matching Socks

Mr. P has 4 black socks and 14 white socks in his drawer.

(1) How many socks must he pick to be certain that two of them match?

(2) What is the probability that he will pick two matching socks if he draws out two socks at random (without looking)?

Solution to the Problem:

(1) 3 socks

(2) The probability is 97 / 153 or .634 or 63.4%.

There are 153 different ways in which 2 socks (out of 18) can be chosen:
₁₈ C ₂ = (18!) / (2! * (18 - 2)!) = 153

There are 91 different ways in which 2 white socks can be chosen:
₁₄ C ₂ = (14!) / (2! * (14 - 2)!) = 91

There are 6 different ways in which 2 black socks can be chosen:
₄ C ₂ = (4!) / (2! * (4 - 2)!) = 153

So, there are 91 + 6 ways in which matching socks can be drawn.

The probability is 97 / 153.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Mike Bova	Wallingford, Connecticut
3. Alex Jeon	----------

Send any comments or questions to: David Pleacher