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In an election there are 8 candidates, out of which 5 are to be choosen. If a voter may vote for any number of candidates but not greater than the number to be choosen, then in how many ways can a voter vote:

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219

216

114

218

answer is C.

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Detailed Solution

Required number of ways

$\begin{aligned} =^{8} C_{1} +^{8} C_{2} +^{8} C_{3} +^{8} C_{4} +^{8} C_{5} \\ = 8 + 28 + 56 + 70 + 56 = 218 \end{aligned}$

{Since voter may vote to one, two, three, four or all candidates}

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