SOLUTION: Help!
A woman has 11 close friends. In how many ways can she invite 5 of them for dinner, if there are 2 who are not in good talking terms and so both can not be at the dinner, b
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Question 1146066: Help!
A woman has 11 close friends. In how many ways can she invite 5 of them for dinner, if there are 2 who are not in good talking terms and so both can not be at the dinner, but at most one of them can be invited?
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
There are 9 "regular" friends and 2 "other" friends. ("Other" friends are friends that cannot both be invited at the same time.) The woman can invite the following combinations:
5 regular friends and 0 other friends
4 regular friends and 1 other friend
Ways to invite 5 regular friends and 0 other friends:
9C5 = = 126
Ways to invite 4 regular friends and 1 other friend:
9C4 * 2C1 = * = 126 * 2 = 252
So...there are a total of 126 + 252...or 378 ways she can do the invites.
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