Q. In a club election the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be 126, then the number of contestants is
A) 4
B) 5
C) 6
D) 7
Explanation
(d)
Let the total number of contestants$= n$
A voter can vote to $(n - 1)$ candidates
$\therefore\ \ ^{n}C_{1} + \ldots + \ ^{n}C_{n - 1} = 126$
$\Rightarrow \ \ \ \ 2^{n} - 2 = 126$
$\Rightarrow \ \ \ \ 2^{n} = 128 = 2^{7}$
$\Rightarrow \ \ \ \ n = 7$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.