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

Answer 1

The correct option is C

$385$

Explanation for the correct option:

Given:

Total number of candidates $=10$

Number of candidates to be selected $=4$

$\therefore$Required number of ways in which a voter can vote for at least one candidates $={}^{10}C_1+{}^{10}C_2+{}^{10}C_3+{}^{10}C_4$

$=\frac{10!}{1!.9!}+\frac{10!}{2!.8!}+\frac{10}{3!.7!}+\frac{10!}{4!.6!}$

$=10+45+120+210$

$=\mathbf{385}$

Hence, Option ‘C’ is Correct.