3. Ms. Lawton is redecorating her office. She has a choice of 5 colors of paint, 3 kinds of curtains, and 4 colors of carpet. How many different ways are there to redecorate?

7 answers

To find the total number of ways to redecorate, you would multiply the number of options for each category together.

5 colors of paint x 3 kinds of curtains x 4 colors of carpet = 60 different ways to redecorate.

Therefore, Ms. Lawton has 60 different ways to redecorate her office with the given choices.
how did you get that answer
To find the total number of ways to redecorate, you can use the fundamental counting principle, which states that if there are \(n_1\) ways to do the first task, \(n_2\) ways to do the second task, and so on, then there are a total of \(n_1 \times n_2 \times \ldots\) ways to do all the tasks.

In this case, there are 5 colors of paint, 3 kinds of curtains, and 4 colors of carpet. So, the total number of ways to redecorate is:

\(5 \text{ colors of paint} \times 3 \text{ kinds of curtains} \times 4 \text{ colors of carpet} = 5 \times 3 \times 4 = 60\)

Therefore, there are 60 different ways to redecorate Ms. Lawton's office using the given choices.
how?
To break it down step by step:

1. Ms. Lawton has 5 choices for the color of paint.
2. For each choice of paint color, she has 3 choices for the kind of curtains.
3. For each combination of paint color and curtain type, she has 4 choices for the color of carpet.

To calculate all the possible combinations, you multiply the number of choices for each category together:

5 (colors of paint) x 3 (kinds of curtains) x 4 (colors of carpet) = 60

So, there are 60 different ways Ms. Lawton can redecorate her office by choosing from the 5 colors of paint, 3 kinds of curtains, and 4 colors of carpet available to her.
oh okay, thanks
You're welcome! If you have any more questions or need further clarification, feel free to ask. I'm here to help!