Unformatted text preview: s is either Cn ,r or ȹ ȹ , and is ȹ r Ⱥ
€
pronounced verbally as “n choose r”. So the relationship between the two is Cn ,r = ar,n − r . So we will switch to the standard notation. €
€
Definition: For all nonnegative integers, n and r, define Cn ,r by (1) Cn ,r = 1 if r = 0 or n and (2) Cn ,r = Cn −1.r −1 + Cn −1,r for all n > 0. Problem. Using only the definition, use induction to prove the formula €
€
n!
Cn ,r =
. €
r!( n − r)!
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 Winter '11
 JamesKing
 Math

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