Chapter 8.2, Problem 8.42E

(a)

To determine

To calculate the number of ways that the program can choose who answers these three questions.

Answer to Problem 8.42E

  $21952$ possibilities.

Explanation of Solution

Use the multiplication counting principle and that there are $28$ students:

  $28\times 28\times 28=21952$

(b)

To determine

To calculate the number of ways in which three different students are chosen to answer these three questions.

Answer to Problem 8.42E

  $19656$ possibilities.

Explanation of Solution

Since order is important we need to use a permutation:

  $\begin{array}{l}P{}_3=\frac{28!}{(28-3)!}\\ =28\times 27\times 26\\ =19656\end{array}$

(c)

To determine

To calculate the probability that the program selects three different students in the class for the first three questions.

Answer to Problem 8.42E

  $89.54\%$

Explanation of Solution

The probability is then:

  $\begin{array}{l}\frac{19656}{21952}=0.8954\\ =89.54\%\end{array}$