Final answer:
There are 42 ways a voter can cast their vote in an election with 3 positions to be filled from 6 candidates. This considers all combinations of voting for 1, 2, or 3 candidates as well as not voting at all.
Step-by-step explanation:
The question asks how many different ways a voter can cast their vote if there are 3 positions to be filled from 6 candidates. A voter can vote for up to 3 candidates but not more. This problem can be solved using combinational mathematics.
The total number of ways the voter can cast the vote is the sum of the number of ways they can vote for 1, 2, or 3 candidates from the 6 available, since they can choose not to use all of their votes. This is calculated as the combination of 6 candidates taken 1 at a time, 2 at a time, and 3 at a time, plus the option to cast no votes.
- For choosing 1 candidate: C(6,1) = 6
- For choosing 2 candidates: C(6,2) = 15
- For choosing 3 candidates: C(6,3) = 20
Don't forget to include the possibility of casting no vote, which is 1 way. So the final calculation is 6 + 15 + 20 + 1 = 42 ways to cast a vote. Therefore, the correct number of ways a voter can cast their vote is 42, though this option is not listed in the given choices. It seems that there might be an error with the provided options.