Everyone thought that Martha Mathy was trying to start a new fashion trend when she started wearing socks that did not match. her "look" started to catch on, and pretty soon all the kids at her school were wearing mixed-up socks, too. Rita Writer, a reporter for the school paper, interviewed Martha about the new sock trend. " Wat gave you the idea to wear mismatched socks?" Rita Asked. "Its simple mathematics," Martha replied. "you see, I have 18 socks at home but no two are the same. with just these 18 socks, I can create over 100 unique pairs of mismatched socks." Rita found this hard to believe, so she checked it out. Was Martha correct?

There are 153 combinations

Combinations - any two from eighteen is given by the formula 18C2 or 18! / (2!*16!)

= 18 * 17 / 2 = 153

OK that is the maths - now the explanation

The first sock can be any of 18

The second sock can be any of 17 (one already been selected and they must be mismatched)

Therefore there are 18*17 = 306 permutations she could make

However the question asks for "combinations" not "permutations"

A green sock on the right foot and a yellow sock on the left foot is deemed to be a different "permutation" to a yellow sock on the right foot and a green sock on the left foot. HOWEVER, they are regarded as the same "combination" in both cases you have one green and one yellow sock.

Therefore for combinations we must divide the 306 permutations calculated above by 2 = 153

FYI Walton has incorrectly given you the value of 18!. That would only apply if Martha Mathy had 18 feet!