Combinations: nine friends, three couples, three single, w/

[jessica098]

Could anyone help me with this problem dealing with combinations??

A woman has nine close friends. In how many ways can she invite six of these to dinner if the friends consist of three single people and three married couples and, if a husband or wife is invited, the spouse must be invited too.

I know that she can invite six of her nine friends in 84 different ways (9C6) but i dont know how to figure out the number of ways if three are single and three are married couples?

Any help would be greatly appreciated! Thanks!

 

[Deleted member 4993]

Re: Combinations

Could anyone help me with this problem dealing with combinations??

A woman has nine close friends. In how many ways can she invite six of these to dinner if the friends consist of three single people and three married couples and, if a husband or wife is invited, the spouse must be invited too.

I know that she can invite six of her nine friends in 84 different ways (9C6) but i dont know how to figure out the number of ways if three are single and three are married couples?

Any help would be greatly appreciated! Thanks!

She can invite 3 couples

She can invite 2 single and 2 couple

Now for each catagory - how many ways she can invite people? Add those up...