So the relationship between the two is cn r arn r

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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)! Prob...
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