Posted by Joel on November 07, 2002 at 09:45:39:
In Reply to: ok; here tizz: posted by Denis Borris on November 07, 2002 at 02:30:05:
: : DEFINITELY the answer is: the number of ways to select any committee of 5 out of 16 people, minus the number of ways to select a committee with NO women, so
: : C(16,5) - C(9,5) = 16!/5!11! - 9!/5!4! = 4242
: DEFINITELY AGREE!!
: : But, why don't I get the same answer if I say: number of ways to select 1 women out of 7 times number of ways to select any 4 people out of the remaining 15:
: : C(7,1) * C(15,4) = 7 * 15!/4!11! = 9555 clearly wrong, but who's getting double-counted here?
: Here, you are committeedly inflating (!) by throwing that 1st woman back in;
: then the 2nd woman back in.....
: So it should be:
: 15!/4!11! + 14!/4!10! +.....+ 9!/4!5! = 4242
: You worded that a bit like " the 3 guys renting 3 rooms....where's the missing
: dollar?" puzzle; did you do that on purpose?!
: Ya sure had me spinning around for a while :)
Thank you Mr. B. Excellent analysis! (You don't really think I'm that devious, do you?) :)