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

Question

In an election, the number of candidates is one greater than the persons to be elected. If a voter can vote in 254 ways, the number of candidates is (A) 7 (B) 10 (C) 8 (D) 6

Tardigrade Admin · Accepted Answer

Let there be n candidates. Then n C1+ n C2+⋅s+ n Cn-1=254 ⇒ 2n-2=254 or 2n=28 or n=8

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

7

10

8

6

Let there be $n$ candidates. Then
$^{n} C_{1} +^{n} C_{2} + \dots +^{n} C_{n - 1} = 254$
$\Rightarrow 2^{n} - 2 = 254$
or $2^{n} = 2^{8}$ or $n = 8$

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

7

10

8

6

Let there be n candidates. Then nC1​+nC2​+⋯+nCn−1​=254 ⇒2n−2=254 or 2n=28 or n=8

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

Let there be $n$ candidates. Then
$^{n} C_{1} +^{n} C_{2} + \dots +^{n} C_{n - 1} = 254$
$\Rightarrow 2^{n} - 2 = 254$
or $2^{n} = 2^{8}$ or $n = 8$