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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 elected. If a voter votes for at least one candidate, then the number of ways he can vote is (a) 385 (b) 1110 (c) 5040 (d) 6210 |
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Answer» (a) 385 As there are 4 candidates to be elected and the voter votes for at least one candidate, the voter can vote for 1 or 2 or 3 or 4 candidates out of 10 candidates. ∴ Total number of ways in which the voter can vote = 10C1 + 10C2 + 10C3 + 4C4 = \(10+\frac{10\times9}{2\times1}+\frac{10\times9\times8}{3\times2\times1}+\frac{10\times9\times8\times7}{4\times3\times2\times1}\) = 10 + 45 + 120 + 210 = 385. |
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