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Find the number of combinations. In how many ways can 11 contestants for an award be narrowed down to 3 finalists?

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There are 11 contestants and only 3 finalists to be narrowed down

No of ways =11C3\textbf{No of ways }=11C_{3}

=11!3!×(113)!=11×5×3=165\begin{align*} &=\dfrac{11!}{3!\times{(11-3)!}}\\ \\ &=11\times5\times3\\ \\ &=165 \end{align*}

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