SOLUTION: A woman has 11 friends and she would like to invite 5 of them for a get together, in how many ways can this be done if 2 of her 11 friends are not on speaking terms and will not at
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Question 1126530: A woman has 11 friends and she would like to invite 5 of them for a get together, in how many ways can this be done if 2 of her 11 friends are not on speaking terms and will not attend together? Answer by ikleyn(52781) (Show Source):
In all, there are = = 462 ways to form group of 5 from 11 items (persons).
Of them, those groups are prohibited (and must be subtracted from 462) that contain these two special friends.
So we need to count the number of such groups.
The number of such groups is exactly the number of ways you can complement these two special persons to the group of 5,
by adding 3 other persons from 11-2 = 9 remaining.
You can do it in = = 84 ways.
So, the answer to the problem question is this difference
462 - 84 = 378.
