Question

13. At an election there are 5 candidates and 3 members are to be elected. A voter is entitled
to vote for any number of candidates not greater than the number to be elected
number of ways a voter choose to vote is :
(a) 20
(b) 22
(c) 25
(d) none of these
​

Answer 1

Given:

Total candidates = 5

Candidates to be elected = 3

To Find:

Number of ways a voter can choose to vote

Solution:

A voter can put the votes as =  1 vote, 2 votes or 3 votes.  

Total number of ways to give only 1 vote = 5C1 = 5  

Total number of ways to give only 2 vote = 5C2 = 10  

Total number of ways to give all 3 vote = 5C3 = 10

Therefore, total ways a voter can vote will be -

5C1 + 5C2  + 5C3

= 5 + 10 + 10

= 25

Answer: Thus, the voter can vote in 25 ways