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Permutations And Combinations

Question

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Compute:

$fraction numerator straight n factorial over denominator left parenthesis straight n minus 2 right parenthesis factorial end fraction$

Solution

fraction numerator straight n factorial over denominator left parenthesis straight n minus 2 right parenthesis factorial end fraction space equals space fraction numerator straight n cross times left parenthesis straight n minus 1 right parenthesis cross times left parenthesis straight n minus 2 right parenthesis factorial over denominator left parenthesis straight n minus 2 right parenthesis factorial end fraction equals space straight n left parenthesis straight n minus 1 right parenthesis.

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