First slide

Combinations

Question

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

Difficult

A

$^{n} C_{3} - n \cdot (n - 4)$
B

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

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

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

Solution

No of ways of selecting three vertices $=^{n} c_{3}$
No of ways of selecting three consecutive vertices $= n$

No of ways of selecting two consecutive vertices $= n (n - 4)$

$=^{n} c_{3} - n - n (n - 4)$

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