Question

question 5 of 6
mrs. mortlock uses a calculator program to select students at random to answer questions during class. each of the 28 students in her class is equally likely to be chosen every time she runs the program. suppose mrs. mortlock runs the program for five different questions.
(a) in how many different ways can the program select which students will answer the five questions?
(b) how many of the selections in part (a) include 5 different students?

Explanation:

Step1: Solve part (a)

Since each question has 28 possible students to be chosen, and there are 5 questions. By the multiplication principle, the number of ways is \(28\times28\times28\times28\times28 = 28^{5}\).

$$28^{5}=28\times28\times28\times28\times28=17210368$$

Step2: Solve part (b)

For the case of 5 different students, we use the permutation formula \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 28\) and \(r=5\).

$$P(28,5)=\frac{28!}{(28 - 5)!}=\frac{28!}{23!}=28\times27\times26\times25\times24=1179360$$

Answer:

(a) \(17210368\)
(b) \(1179360\)