4. Probability

Counting

4. Probability

Counting

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Multiple Choice

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?

$2197$

$1716$

$13$

$6$

Verified step by step guidance

Identify the number of positions to be filled: president, vice president, and treasurer. This means there are 3 positions to fill.

Recognize that the order in which these positions are filled matters, as each position is distinct (president, vice president, treasurer). This is a permutation problem.

Determine the number of members available to fill these positions, which is 13.

Use the permutation formula to calculate the number of ways to arrange 13 members into 3 positions. The formula for permutations is:

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.

Substitute the values into the permutation formula:

P (13, 3) = \frac{13!}{(13 - 3)!}

. Calculate the factorials to find the number of permutations.

7:11m

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