# ok; here tizz:

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Posted by Denis Borris on November 07, 2002 at 02:30:05:

In Reply to: selecting a committee posted by Joel on November 06, 2002 at 23:22:11:

: 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 :)

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