No. of TRIANGLES...

Probability Level 2

Let T n 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 T_{n+1} - T_{n} = 10 then the value of n is

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8 10 7 5

Harshvardhan Mehta by Harshvardhan Mehta , 23, India

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2 solutions

T n = n C 3 T_{n} = ^{n}C_{3}

⇒ T n + 1 = n + 1 C 3 \Rightarrow T_{n+1} = ^{n+1}C_{3}

Therfore,

T n + 1 − T n = n + 1 C 3 − n C 3 T_{n+1} - T_{n} = ^{n+1}C_{3} - ^{n}C_{3}

⇒ n C 2 = 10 \Rightarrow ^{n}C_{2} = 10

⇒ n = 5 \Rightarrow \boxed{n = 5}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

good thing you gave choices to the question #RevEngr

Vincent Miller Moral - 6 years, 1 month ago
Rishabh Jain
Jul 26, 2014

n+1C3 - nC3=10 => n(n-1)=10 =>n=5

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