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
Correct Answer: CShow Answer
Answer:
Solution:
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 $ .