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?
For the first essay, she has 5 choices. For the second, she cannot repeat the same topic, so she is left with 5-1=4 choices.
By the multiplication principle, she has ? choices?
20
Correct!
To determine the number of ways that Macawi can choose the topics for the two essays, we can use the concept of combinations.
To start, we need to determine the number of choices Macawi has for the first essay. Since there are 5 topics to choose from, she can select any one of the 5 topics for her first essay.
For the second essay, Macawi must choose a different topic from the list. Therefore, there are only 4 topics remaining for her to choose from.
To calculate the total number of ways to choose the topics for the two essays, we multiply the number of choices for the first essay by the number of choices for the second essay:
Number of ways = number of choices for first essay * number of choices for second essay
= 5 * 4
= 20
Therefore, there are 20 ways for Macawi to choose the topics for her two essays.