Chapter 8.2, Problem 8.41E

(a)

To determine

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

Answer to Problem 8.41E

  $784$ possibilities.

Explanation of Solution

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

  $28\times 28=784$

(b)

To determine

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

Answer to Problem 8.41E

  $756$ possibilities.

Explanation of Solution

Since order is important we need to use a permutation:

  $\begin{array}{l}P{}_2=\frac{28!}{(28-2)!}\\ =28\times 27\\ =756\end{array}$

(c)

To determine

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

Answer to Problem 8.41E

  $96.43\%$

Explanation of Solution

The probability is then:

  $\begin{array}{l}\frac{756}{784}=0.9643\\ =96.43\%\end{array}$