Question

An elementary school teacher assigns classroom jobs to three students each week. One student hands out craft supplies, one erases the chalkboard, and one takes messages to the office. How many different ways can the teacher assign these three jobs to 24 students in the class?

a) 1 way
b) 24 ways
c) 72 ways
d) 1,768 ways

Answer 1

There are 12,144 different ways the teacher can assign three distinct classroom jobs to 24 students, as this is based on the permutations formula P(n, k) = n! / (n - k)!.

Step-by-step explanation:

The student is asking how many different ways the teacher can assign three distinct classroom jobs to 24 students. This is a permutation problem because the order in which the students are assigned to the jobs matters. The formula for permutations is P(n, k) = n! / (n - k)!, where n is the total number of items to choose from, which is 24 in this case, and k is the number of items to choose, which is 3 here. The calculation is thus:

1. Calculate the factorial of 24, which is 24!.
2. Calculate the factorial of the difference between 24 and 3, which is 21!.
3. Divide the factorial of 24 by the factorial of 21 to find the number of permutations.

The calculation would be P(24, 3) = 24! / (24 - 3)! = 24! / 21! = 24 × 23 × 22 = 12,144. Therefore, there are 12,144 different ways the teacher can assign these jobs to the students.