^ n C _ 9 =^ n C _ 8 n!9!(n 9)!=n!8!(n 8)! (n 8)(n 9)!(n 9)!=9!8! n 8=9 n=17 ^nC_17=^17C_17=17!17!0!=1 ...

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Combination

nC9=nC8 find ...

Question

$^{n} C_{9} =^{n} C_{8}$ find $^{n} C_{17}$ .

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Solution

$^{n} C_{9} =^{n} C_{8} \frac{n!}{9! (n - 9)!} = \frac{n!}{8! (n - 8)!} \frac{(n - 8) (n - 9)!}{(n - 9)!} = \frac{9!}{8!} n - 8 = 9 n = 17$
$^{n} C_{17} =^{17} C_{17} = \frac{17!}{17! 0!} = 1$

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