In an election number of candidates is 1 greater than persons to be elected. If a voter can vote in

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6.Permutation and Combination

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

A

$7$

B

$10$

C

$8$

D

$6$

Solution

(c) Let there are $n$ candidates then

$^n{C_1}{ + ^n}{C_2} + ……{ + ^n}{C_{n – 1}} = 254$

$ \Rightarrow $ ${2^n} – 2 = 254$

$ \Rightarrow $ ${2^n} = {2^8}$

.$ \Rightarrow $ $n = 8$.

Standard 11

Mathematics

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