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Let $P_{n}$ denote the number of ways of selecting 3 people out of n sitting in a row, if no two of them are consecutive and $Q_{n}$ is the corresponding figure when they are in a circle. If $P_{n} {-Q}_{n} =6$ , then n is equal to:

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answer is C.

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Detailed Solution

$P_{n} =^{n - 2} C_{3}; Q_{n} =^{n} C_{3} - [n + n (n - 4)]$
or $Q_{n} = \frac{^{n} C_{1} \cdot^{n - 4} C_{2}}{3}$
$P_{n} - Q_{n} = 6$
$\Rightarrow n = 10$

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