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 total number of members available for selection, which is 13.
2. Understand that the positions of president, vice president, and treasurer are distinct, meaning the order of selection matters.
3. Use the concept of permutations to determine the number of ways to fill these positions. The formula for permutations is given by: $P(n,r)=\frac{n!}{(n-r)!}$, where n is the total number of items to choose from, and r is the number of items to choose.
4. Substitute the values into the permutation formula: $P(13,3)=\frac{13!}{(13-3)!}$.
5. Calculate the factorial values and simplify the expression to find the number of ways to fill the positions.