I have the following combinatoric problem (well it's actually a probability problem that need to be resolved using combinatorics):
There are pairs of shoes in the closet.
shoes are chosen from it randomly. ( )
find the probability to get exactly pairs.
so this is what I'm thinking:
first of all: (the number of possibilities to choose 2m shoes from 2n).
but I just can't decide how many possibilities are there to choose exactly pairs out of .
at first I thought it would be , but that's not the right answer...
any help would be greatly appretiated.
btw, acoording to what I found somwehre online, the answer is
I just couldn't figure out why...