Question

# Let $$T_{n}$$ be the number of all possible triangles formed by joining vertices of an $$n$$-sided regular polygon. If $$T_{n+1}-T_{n}=10$$, then the value of $$n$$ is

A
5
B
10
C
8
D
7

Solution

## The correct option is A 5we know that a triangle needs $$3$$ vertices to be formed so out of $$n$$ vertices $$3$$ should be chosen$$=\ ^nC_3$$According to the given condition, we can write that$$^{n+1}C_{3}-^{n}C_{3}=10$$$$\Rightarrow ^{n}C_{2}=10$$$$\Rightarrow n=5$$Maths

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