Question

In an election, the number of candidates is one more than the number of members to be elected. A voter can cast any number of the vote but not more than the candidates to be elected and not less than 1 vote. If a voter can cast his vote in $30$ ways, then the number of the candidates is

• A. $4$
• B. $5$
• C. $6$
• D. None of these

Answer 1

The correct option is A $4$

Voter can cast his vote in $30$ ways

A voter can cast any number of the vote but not more than the candidates to be elected and not less than 1 vote

i.e.${}^{m+1}{\text{C}}_{0}an{d}^{m+1}{\text{C}}_{(}m+1)$ will not be incuded

$\therefore$ A voter can vote a candidate or cannot vote a candidate

$\therefore$ Total no. of ways will be 2^{m+1}-2=30$

$2^{m+1}=32$

m=4,Answer