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?

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**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 91-7 = 84 ways

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

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

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**Damon**, Tuesday, November 16, 2010 at 7:10pm
excuse typo

2! = 2*1 = 2

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**Damon**, Tuesday, November 16, 2010 at 7:11pm
combinations is

n!/[ (n-r)! r! ]

here n=14

r = 2

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**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

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**kitkat**, Tuesday, November 16, 2010 at 7:27pm
what I did is

Total= 14*13=182

Matched pairs=7*2=14

182-14- 168 possibilities

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**Damon**, Tuesday, November 16, 2010 at 8:09pm
but you can not tell left-right

from

right-left

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**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

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