Question 8. Jackie has 14 close friends. Find the number of ways she can invite 5 of them to dinner under the following conditions:
A. There are no restrictions.
B. Two of the friends are married to each other and will not attend separately.
C. Two of the friends are not speaking to each other and will not attend together.
So for no restrictions I think it would just be 14 choose 5.For B, I think it would be 14 choose 5 minus 10 because for each of the 5 "slots" that a friend could take up if one of them is from the married couple and the other isn't there it is a null possibility hence it is subtracted. For C, I think it would be 14 choose 5 minus 5 because there are 5 "slots" and if there are both people present in this set of 5, then that option would be subtracted. Am I going about this correctly? Thanks.