Permutations And Combinations Question 74
Question: Let $ T _{n} $ denote the number of triangles which can be formed using the vertices of a regular polygon of $ n $ sides. If $ {T _{n+1}}-T _{n}=21, $ then $ n $ equals [IIT Screening 2001]
Options:
A) 5
B) 7
C) 6
D) 4
Correct Answer: B
Show Answer
Answer:
Solution:
Þ $ ({{}^{n}}C_3+{{}^{n}}C_2)-{{}^{n}}C_3=21 $ \ $ ^{n}C_2=21 $ or $ n(n-1)=42=7.6\therefore n=7 $ .
BETA
