In a club election,the number of contestants | vedclass

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(C) Let the number of candidates be $n$.According to the problem,the maximum number of candidates a voter can vote for is $n-1$.The total number of wa

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) Let the number of candidates be $n$.According to the problem,the maximum number of candidates a voter can vote for is $n-1$.The total number of ways a voter can vote is the sum of combinations of choosing $1, 2, 3, \dots, n-1$ candidates from $n$ candidates.This is given by: $^{n}C_{1} + ^{n}C_{2} + ^{n}C_{3} + \dots + ^{n}C_{n-1} = 62$.We know the identity: $^{n}C_{0} + ^{n}C_{1} + ^{n}C_{2} + \dots + ^{n}C_{n} = 2^{n}$.Substituting $^{n}C_{0} = 1$ and $^{n}C_{n} = 1$,we get: $1 + (^{n}C_{1} + ^{n}C_{2} + \dots + ^{n}C_{n-1}) + 1 = 2^{n}$.$1 + 62 + 1 = 2^{n}$.$64 = 2^{n}$.$2^{6} = 2^{n}$.Therefore,$n = 6$.

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 is $62$,then the number of candidates is:

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