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Sixteen men compete with one another in running, swimming and riding. How many prize lists could be made, if there were altogether 6 prizes of different values, one for running, 2 for swimming and 3 for riding?

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$16 \times 15 \times 14$

$16^{3} \times 15^{2} \times 14$

$16^{3} \times 15 \times 14^{2}$

$16^{2} \times 15 \times 14$

answer is B.

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Detailed Solution

Number of ways of giving one prize for running = 16
Number of ways of giving two prizes for swimming =16x15
Number of ways of giving three prizes for riding =16x15x14
Required ways of giving prizes

$\begin{matrix} = 16 \times 16 \times 15 \times 16 \times 15 \times 14 \\ = 16^{3} \times 15^{2} \times 14 \end{matrix}$

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