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Question
Prove that:
Solution
\[ LHS = \frac{n!}{(n - r)!}\]
\[ = \frac{n\left( n - 1 \right)\left( n - 2 \right)\left( n - 3 \right)\left( n - 4 \right) . . . \left( n - r + 1 \right)\left[ \left( n - r \right)! \right]}{(n - r)!}\]
\[ = n\left( n - 1 \right)\left( n - 2 \right)\left( n - 3 \right)\left( n - 4 \right) . . . \left( n - r + 1 \right)\]
\[ = n\left( n - 1 \right)\left( n - 2 \right)\left( n - 3 \right)\left( n - 4 \right) . . . \left[ n - \left( r - 1 \right) \right] = RHS\]
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