math

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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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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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Why did you divide the answer from 14*13 by 2?

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23! = 2*1 = 2

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excuse typo
2! = 2*1 = 2

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combinations is
n!/[ (n-r)! r! ]
here n=14
r = 2

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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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what I did is
Total= 14*13=182
Matched pairs=7*2=14
182-14- 168 possibilities

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but you can not tell left-right
from
right-left

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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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