In a club election number of contestants is one more than number of maximum candidates for

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6.Permutation and Combination

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In a club election the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be $62,$ then the number of candidates is :-

A

$7$

B

$5$

C

$6$

D

None of these

Solution

Let there aer $n$ candidates

$^{n} C_{1}+^{n} C_{2}+^{n} C_{3}+\cdots+^{n} C_{n-1}=62$

$\Rightarrow 2^{\mathrm{n}}-2=62 \Rightarrow 2^{\mathrm{n}}=64 \Rightarrow \mathrm{n}=6$

Standard 11

Mathematics

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