A gym coach must select 11 seniors to play on a football team. If he can make his selections in 12,376 ways, how many seniors are eligible to play?
I am having troubles with this question. Can anyone help me? Thanks.
2007-12-06 05:16:07 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Basically the question is asking if you start with N players and choose 11, there are 12,376 ways to do that.
C(N, 11) = 12,376
Now solve for N.
The formula for C(n, k) is:
.... n!
-----------
(n-k)! k!
In your case:
..... n!
---------------- = 12,376
(n - 11)! 11!
The factors of 12,376 are: 2 x 2 x 2 x 7 x 13 x 17, so I highly suspect the answer is 17.
Indeed:
..17!
--------
6! 11!
17 x 16 x 15 x 14 x 13 x 12
-------------------------------------
6 x 5 x 4 x 3 x 2 x 1
With some cancelling you get:
17 x 2 x 1 x 7 x 13 x 4 = 12,376
Answer:
The coach was choosing from 17 eligible seniors to get the 11 players.
2007-12-06 05:18:58 · answer #1 · answered by Puzzling 7 · 2⤊ 0⤋
11
2007-12-06 05:18:54 · answer #2 · answered by Anonymous · 0⤊ 2⤋
nC11 = 12376
n!/[(n-11)!11!] =12376
Solve for n
2007-12-06 05:30:23 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
1,126
2007-12-06 05:18:41 · answer #4 · answered by Anonymous · 0⤊ 2⤋