A committee of 12 students must select from their group a president, a vice-president, and a secretary. In how many possible ways can this be accomplished?
12*11*10
To determine the number of possible ways the committee can select a president, a vice-president, and a secretary from a group of 12 students, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations when selecting three students from a group of 12.
To find the number of permutations, we follow these steps:
Step 1: Determine the number of choices for each position.
- For the president position, there are 12 students to choose from.
- For the vice-president position, after selecting one student for the president position, there remain 11 students to choose from.
- For the secretary position, after selecting students for the president and vice-president positions, there remain 10 students to choose from.
Step 2: Multiply the number of choices for each position.
- Number of choices for the president position: 12
- Number of choices for the vice-president position: 11 (since one student has been chosen for the president position)
- Number of choices for the secretary position: 10 (since two students have been chosen for the president and vice-president positions)
Step 3: Calculate the total number of permutations by multiplying the number of choices for each position.
- Total number of permutations = 12 * 11 * 10 = 1320
Therefore, there are 1320 possible ways for the committee to select a president, a vice-president, and a secretary from a group of 12 students.