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# Team game - pairing probability issue (non-academic problem)

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1. So I'm playing a two team game.There are 20 players initially and we know that the makeup of team A is 16 players and team B is 4 players.

Assuming random selection), given each player is 'attached' to another player into pairs, in a way not related to the teams A or B, what is the probability of an A-A pair, a A-B pair and a B-B pair please?
2. P(A) = 4/5
P(B) = 1/5
N = 20

P(A-A) = 4/5 * 4/5 = 1/5
P(A-B) = 4/5 * 1/5 = 4/25
P(B-B) = 1/5 * 1/5 = 1/25

So that's the probability for the first draws, I think. Where do I go from here?

edit: or is it different because there is now 1 less element in the set and so it's not the same probability multiplied by itself?

3. I'd very much appreciate even a methodology here if an answer is too tedious
4. (Original post by BizzStrut)
I'd very much appreciate even a methodology here if an answer is too tedious
This is how I would approach the problem. After being selected a person is removed from the list of people that can be selected.
Therefore the following probabilities occur for the first draw:

Note that there are two permuations for the AB pairing as it can be paired AB or as BA.
Use this principle to now look at the question from a combination standpoint. Any further help needed just ask.

Cryptokyo

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