At an election,a voter may vote for any numbe | vedclass

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(A) The voter can vote for $1, 2, 3,$ or $4$ candidates out of $12$ available candidates.The number of ways to choose $k$ candidates out of $12$ is gi

Vedclass · Accepted Answer

$793$

Vedclass · Answer

(A) The voter can vote for $1, 2, 3,$ or $4$ candidates out of $12$ available candidates.The number of ways to choose $k$ candidates out of $12$ is given by the combination formula ${}^{12}C_k$.Since the voter must vote for at least one candidate,the total number of ways is the sum of selecting $1, 2, 3,$ or $4$ candidates:$	ext{Total ways} = {}^{12}C_1 + {}^{12}C_2 + {}^{12}C_3 + {}^{12}C_4$$= 12 + \frac{12 	imes 11}{2 	imes 1} + \frac{12 	imes 11 	imes 10}{3 	imes 2 	imes 1} + \frac{12 	imes 11 	imes 10 	imes 9}{4 	imes 3 	imes 2 	imes 1}$$= 12 + 66 + 220 + 495 = 793$

At an election,a voter may vote for any number of candidates not exceeding the number to be elected. If $4$ candidates are to be elected out of the $12$ contested in the election and a voter votes for at least one candidate,then the number of ways in which a voter can vote is:

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