Question

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 but not more than 3 to be elected. In how many ways may a voter choose a vote?

a. 10 ways
b. 15 ways
c. 20 ways
d. 25 ways

Answer 1

A voter can choose among 5 candidates in 25 different ways by calculating the combinations for selecting 1, 2, or 3 candidates, which are summed up to determine the total ways of voting. Therefore, the correct answer is d. 25 ways.

Step-by-step explanation:

The student is asking about the number of ways a voter can cast a vote in an election where there are 5 candidates and 3 are to be elected, with the voter choosing up to 3 candidates. This is a question of combinatorics, a branch of mathematics dealing with counting, combination, and permutation of sets.

To solve this, we can use combinations because the order in which the candidates are selected does not matter. A voter can choose to vote for 1, 2, or 3 candidates out of the 5 available candidates.

We calculate the number of ways to choose these using the combination formula, which is C(n, k) = n! / (k!(n - k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial.

The total number of ways a voter can vote can be found by adding the combinations for choosing 1, 2, and 3 candidates from 5:

Adding these up gives us:

5 + 10 + 10 = 25 ways

Therefore, the correct answer is d. 25 ways.