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Combination of r Things from n Things When All Are Not Different

At an electio...

Question

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 the voter votes for atleast one candidate, then the number of ways in which he can vote is

A

5040

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B

6210

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C

385

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D

1110

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Solution

The correct option is C 385
Required number of ways $=^{10} C_{4} +^{10} C_{3} +^{10} C_{2} +^{10} C_{1} = 385$

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