Chapter 0, Problem 24PO

To determine

the ways can she choose the topics of the two essays.

Answer to Problem 24PO

The numbers of ways are 10.

Explanation of Solution

Given information :

It is given that for a college application, Macawi must select one of five topics on which to write a short essay. She must also select a different topic from the list for a longer essay.

In the given event, arrangement does not matter so it is combination.

The number of ways is given by,

  $\begin{array}{c}C{}_2=\frac{5!}{2!\times 3!}\\ =\frac{5\times 4\times 3\times 2\times 1}{2\times 1\times 3\times 2\times 1}ways\\ =10ways\end{array}$

So, the numbers of ways are 10.