In an election,the number of candidates is 1 | vedclass

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Question

(C) Let the number of candidates be $n$. The number of persons to be elected is $n-1$.
A voter can vote for any number of candidates from $1$ to $n-1

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) Let the number of candidates be $n$. The number of persons to be elected is $n-1$.
A voter can vote for any number of candidates from $1$ to $n-1$.
The total number of ways a voter can vote is:
$^nC_1 + {}^nC_2 + \cdots + {}^nC_{n-1} = 254$
We know that:
$\sum_{r=0}^{n} {}^nC_r = 2^n$
Therefore,
$^nC_0 + {}^nC_1 + {}^nC_2 + \cdots + {}^nC_{n-1} + {}^nC_n = 2^n$
Substituting the known values:
$1 + 254 + 1 = 2^n$
$256 = 2^n$
$2^8 = 2^n$
Thus, $n = 8$

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

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