First slide

Combinations

Question

A regular polygon of 10 sides is constructed. No. of ways 3 vertices be selected so that no two vertices are consecutive is

Difficult

A

40
B

50
C

60
D

45

Solution

No of ways of selecting 3 from 10 vertices $=^{10} c_{3} = 120$
Two consecutive $= 10 \times^{6} c_{1} = 60$

Three consecutive $= 10$

$= 120 - 60 - 10 = 50$

$o r$

$= \frac{n (n - 4) (n - 5)}{6} = 50$

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