A rectangle polygon of $n$ sides is constructed. No. of ways $3$ vertices be selected so that no two vertices are consecutive is

^{n} C_{3} - n (n - 4)

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^{n} C_{3} - n - n (n - 4)

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^{n} C_{3} + n - n (n - 4)

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^{n} C_{3} + n (n - 4)

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Solution

The correct option is A $^{n} C_{3} - n (n - 4)$
No. of ways $=$ Total $-$ no. of ways in which two consecutive points are present
No. of ways $= n_{C_{3}} - n_{C_{1}} (n - 4) = n_{C_{3}} - n (n - 4)$

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