Question

For a class project, students must select one topic from a list of 15 choices. They will also choose one presentation method: written report, oral presentation, or making a game.
Use the Fundamental Counting Principle to determine how many different project combinations are possible.

Answer 1

The Fundamental Counting Principle states that if you have multiple choices and you want to find the total number of combinations of those choices, you can multiply the number of options for each choice together.

In this scenario, the choices are:

1. Selecting a topic: There are 15 different topics to choose from.
2. Choosing a presentation method: There are 3 different methods available (written report, oral presentation, or making a game).

To find the total number of different project combinations, we multiply the number of topic choices by the number of presentation method choices:

\[
\text{Total combinations} = (\text{Number of topics}) \times (\text{Number of presentation methods}) = 15 \times 3
\]

Calculating that gives:

\[
15 \times 3 = 45
\]

Thus, the total number of different project combinations is **45**.