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. 6210
• B. 385
• C. 1110
• D. 5040

Answer 1

The correct option is B

385

Explanation for correct answer:

Total Candidates$=10$

Candidates to be selected$=4$

Number of ways in which a voter may vote for atleast one candidates

$={10}_{C1}+{10}_{C2}+{10}_{C3}+{10}_{C4}$

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

$=10+45+120+210$

$=385$

then the number of ways in which he can vote, is $385$

Hence, Option ‘B’ is correct.