Question

In an election, the number of candidates is 1 greater than the persons to be elected. If a voter can vote in 254 ways, by selecting at least one of them , then the number of candidates is

• A. 6
• B. 8
• C. 10
• D. 12

Answer 1

Answer: (B)

$\text { Lemusc Elected person }= x $
$x ^{ x +1} C _1+{ }^{ x +1} C _2+\ldots \ldots{ }^{ x +1} C _{ x }=254 $
${ }^{ x +1} C _0+{ }^{ x +1} C _1+{ }^{ x +1} C _2+\ldots \ldots{ }^{ x +1} C _{ x }+{ }^{ x +1} C _{ x +1}=254+1+1$
${ }^{ x +1}=256 $
$2^{ x +1}=2^8 $
$x +1=8 $
$x =7 \text { elected persons } $
$\text { Number of persons }=7+1=8$