Question

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 is $126$, then the number of contestants is.

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is D

$7$

Explanation for the correct answer:

Finding the number of contestants:

Given, that voter has to vote for at least $1$ candidate and for maximum of $\mathrm{n}-1$ candidates, where $\mathrm{n}$ is the number of candidates.

For each candidate, a voter has two options: to vote or not to vote.

Hence, there would be total $2\mathrm{n}$ ways.
Now, if we exclude the condition where voters will vote none or will vote for all the candidates,

So,

$\begin{array}{rcl}{2}^{\mathrm{n}}-2& =& 126\\ 2^{\mathrm{n}}& =& 128\\ 2^{\mathrm{n}}& =& 2^7\\ \therefore \mathrm{n}& =& 7\end{array}$

Hence, the correct option is D.