I you are in a group of 'x' people - there are x-1 people you can choose your pair from.
So you can choose possible pairs.
For 4 people we have - possible pairs.
Because there are x people in the group you can do it x times, so we have: possible pairs:
For 4 people we have - 3 x 4 = 12 pairs. (the denominator)
Now if you where not there you would not be chosen - so there are now x-1 people playing - substitute x-1 in to the previous formula to get the number of pairs not including 1 person.
If you can simplify this factorial stuff pls do.
This gives probabilites of not being chosen as:
4 people: 3/12
5 people: 12/30
6 people: 30/60
7 people: 60/105
Now to generalise:
n people - choosing m (eg 5 people chosing 2 people)
i thonk there is an error here but im tired - i look again soon.