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)

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