Question

there are 5 pairs of different style shoes. how many ways to choose 5 shoes that contains exactly one pair. noticing that left and right are distinguishable.

Answer 1

I feel like nCp and nPc or whatnot should be involved here but I haven't seen either of them in forever. They are like the long lost brothers of my math.

Answer 2

does the pair have to be a matching pair?

Answer 3

yes the pair should be matching

Answer 4

nvm, that's wrong

Answer 5

10*8*6*4*4

Answer 6

I'm just gonna mark that right because you know what you are doing. TAKE GOOD CARE OF MY BROTHERS.

Answer 7

start with 10 shoes
after that you can only pick from 8
then 6
then 4
then 4 ways to pick the last matching shoe

Answer 8

assuming you are picking them all at the same time

Answer 9

sorry but i dont think its correct, the answer for 7 pairs shoes(nothing else changes) is 420...the answer i got from your way seems too large

Answer 10

sorry the question changes to choose 4 shoes from 7 pairs, and should have one matching pair

Answer 11

its right, for the seven one
you start with 7
after that you can pick 5
then 3
then 1
then 4 to match the pair

Answer 12

so 7*5*3*1*4=420

Answer 13

i'm sorry because for the 7 case the question asked to choose 4 shoes from 7 pairs, not 5...i didn't see the question carefully...and 7 is the number of pairs, totally have 14 shoes with distinguishable left and right

Answer 14

its still the same:
you start with 7
after that you can pick 5
then 3
then 4 to match the pair

7*5*3*4=420