sair wrote:

Hi,

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.

Thanks.

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?