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# At an election a voter may vote for any no. of candidates but not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If every voter votes for atleast one candidate, then no. of ways in which a voter can vote is?

$\begin{array}{1 1} 6210 \\ 5040 \\ 1110 \\ 385 \end{array}$

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## 1 Answer

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No. of candidates = 10
A voter can vote at the most 4 candidates and alteast one candidate.
No. of ways in which he can vote for 1 candidate = $^{10}C_1=10$
No. of ways in which he can vote for 2 candidate = $^{10}C_2=45$
No. of ways in which he can vote for 3 candidate = $^{10}C_3=120$
No. of ways in which he can vote for 4 candidate = $^{10}C_4=210$
$\therefore$ The required no. of ways = $10+45+120+210=385$
answered Aug 13, 2013

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