Permutations And Combinations Question 78

Question: A polygon has 35 diagonals, then the number of its sides is [AMU 2002]

Options:

A) 8

B) 9

C) 10

D) 11

Show Answer

Answer:

Correct Answer: C

Solution:

  • Since $ ^{n}C_2-n=35 $
    Þ $ \frac{n!}{2!(n-2)!}-n=35 $
    Þ $ n(n-1)-2n=70 $
    Þ $ n^{2}-3n=70 $
    Þ $ n^{2}-3n-70=0 $
    Þ $ (n+7)(n-10)=0 $
    Þ $ n=10 $ .