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 atleast 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 $385$

Total candidates $=10$
Candidates to be selected $=4$
Number of ways in which a voter may vote for atleast one candidate $={}^{10}{C}_1+{}^{10}{C}_2+{}^{10}{C}_3+{}^{10}{C}_4$
$=\frac{10!}{1!9!}+\frac{10!}{2!8!}+\frac{10!}{3!7!}+\frac{10!}{4!6!}$
$=10+45+120+210$
$=385$