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

• A. $385$
• B. $1110$
• C. $5040$
• D. $6210$

Answer 1

The correct option is A $385$

Voter can vote either one, two, three of four votes.

Thus desired number of ways is

$=\left(\begin{array}{c}10\\ 1\end{array}\right)+\left(\begin{array}{c}10\\ 2\end{array}\right)+\left(\begin{array}{c}10\\ 3\end{array}\right)+\left(\begin{array}{c}10\\ 4\end{array}\right)$

$\because (\frac{n}{r}){=}^n{C}_r=\frac{n!}{r!\cdot (n-r)!}$

Using, we get

$=10+45+120+210=385$