Posted by kitkat on Tuesday, November 16, 2010 at 6:43pm.
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?

math  Damon, Tuesday, November 16, 2010 at 6:51pm
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 
math  kitkat, Tuesday, November 16, 2010 at 7:02pm
Why did you divide the answer from 14*13 by 2?

math  Damon, Tuesday, November 16, 2010 at 7:10pm
23! = 2*1 = 2

math  Damon, Tuesday, November 16, 2010 at 7:10pm
excuse typo
2! = 2*1 = 2 
math  Damon, Tuesday, November 16, 2010 at 7:11pm
combinations is
n!/[ (nr)! r! ]
here n=14
r = 2 
math  Damon, Tuesday, November 16, 2010 at 7:15pm
14! = 14*13*12 * 11 etc
12! =12*11 etc
so
14!/12! = 14 * 13
now divide that by 2! which is 2 
math  kitkat, Tuesday, November 16, 2010 at 7:27pm
what I did is
Total= 14*13=182
Matched pairs=7*2=14
18214 168 possibilities 
math  Damon, Tuesday, November 16, 2010 at 8:09pm
but you can not tell leftright
from
rightleft 
math  kitkat, Tuesday, November 16, 2010 at 8:43pm
well for the matched pairs part the 7 is the pairs and the 2 is the orders of pairs LR and RL