math
posted by kitkat .
Ryan reaches into his gym bag for a pair of running shoes. If there are seven different pairs of shoes loose in the bag, how many ways can he pick two shoes that do not match?

combinations of 14 things two at a time = 14!/[12!(2!)]=14*13/2 = 7*13 = 91
but some of those are matching, namely 7 pairs, so there are 917 = 84 ways 
Why did you divide the answer from 14*13 by 2?

23! = 2*1 = 2

excuse typo
2! = 2*1 = 2 
combinations is
n!/[ (nr)! r! ]
here n=14
r = 2 
14! = 14*13*12 * 11 etc
12! =12*11 etc
so
14!/12! = 14 * 13
now divide that by 2! which is 2 
what I did is
Total= 14*13=182
Matched pairs=7*2=14
18214 168 possibilities 
but you can not tell leftright
from
rightleft 
well for the matched pairs part the 7 is the pairs and the 2 is the orders of pairs LR and RL