Question

In how many ways can a chairperson, a secretary, and a treasurer be chosen from a group of 10 people, if each person can hold only one position?

• A. 840
• B. 5040
• C. 1240
• D. 720

Hint:

In problems like this, use permutations when the order of selection matters. The formula \( P(n, r) = \frac{n!}{(n - r)!} \) is essential for calculating the number of ways to assign distinct roles or positions.

Answer 1

The Correct Option is D

This is a permutation problem because the positions of chairperson, secretary, and treasurer are distinct. 
We need to calculate how many ways we can assign these 3 positions to 10 people, where each person can hold only one position. 
The formula for permutations is: \[ P(n, r) = \frac{n!}{(n - r)!} \] In this case, \(n = 10\) and \(r = 3\). Thus, the number of ways is: \[ P(10, 3) = \frac{10!}{(10 - 3)!} = 10 \times 9 \times 8 = 720 \] Therefore, the correct answer is 720.