Question

In a club election the number 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 be 62 then the number of candidates is

• A. 7
• B. 5
• C. 6
• D. none of these

Answer 1

Answer: (C)

6

Voter has to vote for at least $1$ candidate and at max $n-1$ candidates.
Here $n$ is the number of candidates.
For each candidate, he has $2$ options: either to vote for him or not to vote for him.
So, number of ways $=2^n$
But we have to subtract $2$ cases when he votes for none of them or he votes for all of them
So, $2^n-2=62$
$2^n=64$
$n=6$