Could sb in detail provide me clear and detail explananation of the following combination problems. I am bit confused about these.
1. A woman has 11 close friends. Find the number of ways she can invite 5 of them to dinner :
a) Where 2 of the friends are married and will not attend separately.
b) Where 2 of the friends are not on speaking terms and will not attend together.
let me try:
a) Let AB represent the couple who won't attend seperately. Two cases:
Case 1- AB invited.
So number of selections possible - 9C3*2C2 = 84
Case 2 - AB not invited
So now number of selections possible - 9C5 = 126
So total selections for a) = 126+84 = 210
b) PQ represents the not-speaking friends. Three cases
Case 1 - P comes and so Q does not come
Number of selections = 1C1*9C4 = 126
Case 2 - Q comes and P does not come
As above, selections = 126
Case 3 - P and Q, both are not invited
Number of selections = 9C5 = 126
So total number of selections for b) = 2*126 + 126 = 378
What is the OA?