a) if jack has 10 friends, in how many ways can he invite 5 of them to dinner.
b) suppose 2 friends dont like each other, and if one is invited, the other cant come.
c) what if 2 of the friends are married and if they invite that friend, the spouse must come.
Rule of products
The Attempt at a Solution
a) I get 10*9*8*7*6 = 30240 ways.
b) I simply subtract one friend initially to get 9*8*7*6*4 = 15120 ways
c) I subtract to 8 friends because their spouses fill the spots of the other 2.
8*7*6*5*4 = 6720 ways
I'm unsure if i'm misinterpreting the question. My method goes by the order in which they are invited..any help is much appreciated