SOLUTION: how many possible ways can a committee of 8 be selected from a group 14

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Question 515571: how many possible ways can a committee of 8 be selected from a group 14
Answer by drcole(72) About Me  (Show Source):
You can put this solution on YOUR website!
The number of ways that k individuals can be selected from a set of N individuals is given by the formula:
C%28N%2C+k%29+=+%28N%21%29%2F%28%28k%21%29%28%28N+-+k%29%21%29%29
where N! = N(N - 1)(N - 2)***(3)(2)(1) (for example, 6! = (6)(5)(4)(3)(2)(1) = 720). So for this problem:

14! = (14)(13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
8! = (8)(7)(6)(5)(4)(3)(2)(1)
The number 14! is very large, but notice that 8! is just the last eight factors of 14!, so since we are dividing 14! by 8!, we can just cancel out those last eight factors and get:

So there are 3003 ways to choose a committee of 8 from a group of 14.