Ways a Voter Can Choose a Vote

Understanding the Scenario:
In this election scenario, there are five candidates and three members are to be elected. A voter is entitled to vote for any number of candidates.

Calculating the Ways:
To determine the ways a voter can choose a vote, we need to consider the number of options the voter has for each member to be elected. Since the voter can choose any number of candidates, there are multiple possibilities to consider.

Possible Scenarios:
1. Voter chooses 0 candidates: This means the voter does not vote for any candidate. There is only 1 way to do this.
2. Voter chooses 1 candidate: The voter can choose any of the 5 candidates, so there are 5 ways to do this.
3. Voter chooses 2 candidates: The voter can choose 2 out of the 5 candidates, so there are 10 ways to do this.
4. Voter chooses 3 candidates: The voter can choose 3 out of the 5 candidates, so there are 10 ways to do this.
5. Voter chooses 4 candidates: The voter can choose 4 out of the 5 candidates, so there are 5 ways to do this.
6. Voter chooses 5 candidates: This means the voter votes for all candidates, there is only 1 way to do this.

Total Ways:
To find the total ways a voter can choose a vote, we sum up the ways from each scenario:
1 (0 candidates) + 5 (1 candidate) + 10 (2 candidates) + 10 (3 candidates) + 5 (4 candidates) + 1 (5 candidates) = 32 ways.
Therefore, a voter can choose a vote in 32 different ways in this election scenario.