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(A) The number of candidates to be elected is $4$ out of $10$. Since a voter can vote for any number of candidates from $1$ to $4$,the total number of

Vedclass · Accepted Answer

$385$

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(A) The number of candidates to be elected is $4$ out of $10$. Since a voter can vote for any number of candidates from $1$ to $4$,the total number of ways is given by the sum of combinations: Total ways $= ^{10}C_1 + ^{10}C_2 + ^{10}C_3 + ^{10}C_4$. Calculating each term: $^{10}C_1 = 10$ $^{10}C_2 = \frac{10 	imes 9}{2 	imes 1} = 45$ $^{10}C_3 = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$ $^{10}C_4 = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} = 210$ Total ways $= 10 + 45 + 120 + 210 = 385$.

In an election,a voter can vote for any number of candidates but not more than the number of candidates to be elected. There are $10$ candidates and $4$ are to be elected. If a voter must vote for at least one candidate,in how many ways can they vote?

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