A student formed a club at their school. They have 13 members, and need to elect a president, vice president, and treasurer. How many ways are there to fill these officer positions?

• A. 2197
• B. 1716
• C. 13
• D. 6

Answer: (B)

Verified step by step guidance

1. Identify the number of positions to be filled: president, vice president, and treasurer. There are 3 positions.
2. Recognize that the order in which these positions are filled matters, as each position is distinct.
3. Use the concept of permutations to determine the number of ways to arrange 13 members into 3 positions. The formula for permutations is given by: P(n, r) = n! / (n-r)! where n is the total number of items to choose from, and r is the number of items to arrange.
4. Substitute the values into the permutation formula: P(13, 3) = 13! / (13-3)! = 13! / 10!
5. Calculate the permutation by simplifying the factorial expression: 13! / 10! = 13 × 12 × 11, which gives the number of ways to fill the positions.