Question

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?

Answer 1

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

Answer 2

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

Answer 3

23! = 2*1 = 2

Answer 4

excuse typo
2! = 2*1 = 2

Answer 5

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

Answer 6

14! = 14*13*12 * 11 etc
12! =12*11 etc
so
14!/12! = 14 * 13
now divide that by 2! which is 2

Answer 7

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

Answer 8

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

Answer 9

well for the matched pairs part the 7 is the pairs and the 2 is the orders of pairs LR and RL