Q8. - Algebra 2

Question

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. How many ways can she choose the topics for the two essays?

Step-by-Step Solution

Answer

There are 20 ways Macawi can choose the topics for the two essays.

Step 1. Given Information.

Given 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.

Step 2. Calculation .

There are 5 ways to select one of five topics on which Macawi can write a short essay.

Since longer essay needs to be on different topic, she has 4 topics left.

 

Hence, there are 4 ways to select one of the four topics on which Macawi can write a longer essay.

By the Fundamental Counting Principle, there are $5\times 4=20$ ways to choose the topics.

Step 3. Conclusion .

Hence, by Fundamental Counting Principle, there are 20 ways Macawi can choose the topics for the two essays.