In his wardrobe, Fred has a total of ten pairs of gloves. He had to pack his suitcase before a business meeting, and he chooses eight gloves without looking at them. We assume that any set of eight gloves has an equal chance of being chosen.
I am told to calculate the likelihood that these 8 gloves do not contain any matching pairs, i.e. that no two (left and right) gloves are from the same pair.
This is what I came up with, that is, the probability of success for each choice:
At first, I was a little confused by the wording but I believe this seems about right.
Is there an alternative way to get the desired probability, e.g. with $1-...$?
Thanks in advance for any feedback.