## Related questions with answers

Question

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

Solutions

VerifiedSolution A

Solution B

Step 1

1 of 2There are 11 contestants and only 3 finalists to be narrowed down

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

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

Step 1

1 of 2Number of ways = [4ex]

$11_{C_{3}}=\dfrac{11!}{3! \times (11-3)!}=165$

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