The bowling team at Lincoln High School must choose a president, vice president, and secretary. If the team has 12 members, how many ways could the officers be chosen?
Question
The bowling team at Lincoln High School must choose a president, vice president, and secretary. If the team has 12 members, how many ways could the officers be chosen?
Solution
This problem can be solved using the concept of permutations in combinatorics.
Step 1: Identify the number of positions to fill and the total number of candidates. Here, we have 3 positions (president, vice president, and secretary) to fill from 12 candidates (team members).
Step 2: Calculate the number of ways to fill the first position. Any of the 12 team members could be chosen as president, so there are 12 possibilities.
Step 3: Calculate the number of ways to fill the second position. After the president has been chosen, there are only 11 team members left, so there are 11 possibilities for vice president.
Step 4: Calculate the number of ways to fill the third position. After the president and vice president have been chosen, there are only 10 team members left, so there are 10 possibilities for secretary.
Step 5: Multiply the number of possibilities for each position to get the total number of ways the officers could be chosen. This is because for each way of choosing a president, there are multiple ways of choosing the other officers. So, the total number of ways is 12 * 11 * 10 = 1320.
So, there are 1320 different ways the officers could be chosen from the 12 team members.
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