C(n,0) = 1Date: 04/22/2003 at 06:50:38 From: Saurav Kumar Subject: Combinations How is C(n,0)=1, where n is an integer? Date: 04/23/2003 at 09:58:36 From: Doctor Samus Subject: Re: Combinations Hi Saurav, To see why C(n,0) = 1, for n an integer, we must look at the formula for C(n,r), when n is an integer, and r is an integer 0 <= r <= n. It is: n! C(n,r) = -------- (where a! = (a)*(a-1)*(a-2)*...*2*1) r!(n-r)! So if r = 0, then we have: n! C(n,0) = -------- 0!(n-0)! n! = -------- (since we define 0! = 1) n! = 1 Another way to think of it is that C(n,r) can be interpreted as the number of ways you can select r elements from a set of n elements. How many ways can we take 0 elements? Only one: by taking none. I hope this helps, and feel free to write back if you have any other questions. - Doctor Samus, The Math Forum http://mathforum.org/dr.math/ |
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