In an election,there are 8 candidates,out of | vedclass

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(C) The voter can choose to vote for $1, 2, 3, 4,$ or $5$ candidates.Since the voter can vote for any number of candidates up to $5$,the total number

Vedclass · Accepted Answer

$218$

Vedclass · Answer

(C) The voter can choose to vote for $1, 2, 3, 4,$ or $5$ candidates.Since the voter can vote for any number of candidates up to $5$,the total number of ways is given by the sum of combinations:$Ways = ^8C_1 + ^8C_2 + ^8C_3 + ^8C_4 + ^8C_5$Using the formula $^nC_r = \frac{n!}{r!(n-r)!}$:$^8C_1 = 8$$^8C_2 = \frac{8 	imes 7}{2 	imes 1} = 28$$^8C_3 = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$$^8C_4 = \frac{8 	imes 7 	imes 6 	imes 5}{4 	imes 3 	imes 2 	imes 1} = 70$$^8C_5 = ^8C_3 = 56$Total ways $= 8 + 28 + 56 + 70 + 56 = 218$.

In an election,there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?

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