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(C) Total number of candidates $= 10$.Number of candidates to be elected $= 4$.$A$ voter can vote for at most $4$ candidates and at least $1$ candidat

Vedclass · Accepted Answer

$385$

Vedclass · Answer

(C) Total number of candidates $= 10$.Number of candidates to be elected $= 4$.$A$ voter can vote for at most $4$ candidates and at least $1$ candidate.The number of ways to vote for $r$ candidates is given by $^{10}C_{r}$.Number of ways to vote for $1$ candidate $= ^{10}C_{1} = 10$.Number of ways to vote for $2$ candidates $= ^{10}C_{2} = \frac{10 	imes 9}{2 	imes 1} = 45$.Number of ways to vote for $3$ candidates $= ^{10}C_{3} = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$.Number of ways to vote for $4$ candidates $= ^{10}C_{4} = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} = 210$.Total number of ways $= 10 + 45 + 120 + 210 = 385$.

At an election,a voter may vote for any number of candidates,not greater than the number to be elected. There are $10$ candidates and $4$ are to be selected. If a voter votes for at least one candidate,then the number of ways in which he can vote is:

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