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. The number of ways in which a voter may vote for at least one candidate is-

• A. $385$
• B. $1110$
• C. $5040$
• D. None of these

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 =${}^{10}{C}_1{+}^{10}{C}_2{+}^{10}{C}_3{+}^{10}{C}_4=\frac{10!}{1!9!}+\frac{10!}{2!8!}+\frac{10!}{3!7!}+\frac{10!}{4!6!}=10+45+120+210=385Ans=385$