Question

In an election, the number of candidates is $1$ greater than the person to be elected. If a voter can vote in $254$ ways, the number of candidates is

• A. $7$
• B. $10$
• C. $8$
• D. $6$

Answer 1

The correct option is C $8$

Let there be n candidates. Then

${}^n{C}_1{+}^n{C}_2+....{+}^n{C}_{n-1}=254$

$\Rightarrow 2^n-2=254$

or $2^n=2^8$ or $n=8$