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If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, then in how many different ways can these candidates be elected to the Board?
- a)6
- b)8
- c)12
- d)16
- e)24
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If the Board of Selectmen contains 4 positions, and if in the current ...
Understanding the Problem
To determine the number of ways to elect candidates to the Board of Selectmen, we have 4 positions and 2 candidates running for each position.
Positions and Candidates
- **Positions**: 4 (let's call them P1, P2, P3, P4)
- **Candidates for Each Position**: 2 (let's denote them as A and B)
Calculating the Combinations
For each position, since there are 2 candidates, you can choose one candidate in the following way:
- **Position P1**: 2 choices (A or B)
- **Position P2**: 2 choices (A or B)
- **Position P3**: 2 choices (A or B)
- **Position P4**: 2 choices (A or B)
Using the Multiplication Principle
To find the total number of combinations for all positions, you multiply the choices for each position:
- Total Ways = Choices for P1 × Choices for P2 × Choices for P3 × Choices for P4
= 2 × 2 × 2 × 2
= 2^4
= 16
Conclusion
Thus, the total number of different ways to elect candidates to the Board of Selectmen is **16**.
The correct answer is option **D**.
To determine the number of ways to elect candidates to the Board of Selectmen, we have 4 positions and 2 candidates running for each position.
Positions and Candidates
- **Positions**: 4 (let's call them P1, P2, P3, P4)
- **Candidates for Each Position**: 2 (let's denote them as A and B)
Calculating the Combinations
For each position, since there are 2 candidates, you can choose one candidate in the following way:
- **Position P1**: 2 choices (A or B)
- **Position P2**: 2 choices (A or B)
- **Position P3**: 2 choices (A or B)
- **Position P4**: 2 choices (A or B)
Using the Multiplication Principle
To find the total number of combinations for all positions, you multiply the choices for each position:
- Total Ways = Choices for P1 × Choices for P2 × Choices for P3 × Choices for P4
= 2 × 2 × 2 × 2
= 2^4
= 16
Conclusion
Thus, the total number of different ways to elect candidates to the Board of Selectmen is **16**.
The correct answer is option **D**.
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If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, then in how many different ways can these candidates be elected to the Board?a)6b)8c)12d)16e)24Correct answer is option 'D'. Can you explain this answer?
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