Question
Jessie's apartment has 3 rooms. She will paint each room a different color. She is choosing between 7 different paint colors.
In how many different ways can Jessie paint her rooms? Enter the answer in the box.
In how many different ways can Jessie paint her rooms? Enter the answer in the box.
Answers
GPT-4o mini
To determine how many different ways Jessie can paint her 3 rooms using 7 different colors, we can treat this as a problem of choosing and arranging colors.
1. For the first room, Jessie has 7 choices of colors.
2. For the second room, since Jessie can only use a different color from the first, she has 6 choices left.
3. For the third room, she will have 5 choices remaining because it must be painted a different color from the first two.
Now, the total number of ways Jessie can choose and arrange the colors for the 3 rooms is given by multiplying the number of choices for each room:
\[
7 \text{ (for the first room)} \times 6 \text{ (for the second room)} \times 5 \text{ (for the third room)} = 7 \times 6 \times 5
\]
Calculating this:
\[
7 \times 6 = 42
\]
\[
42 \times 5 = 210
\]
Therefore, the total number of different ways Jessie can paint her rooms is \( \boxed{210} \).
1. For the first room, Jessie has 7 choices of colors.
2. For the second room, since Jessie can only use a different color from the first, she has 6 choices left.
3. For the third room, she will have 5 choices remaining because it must be painted a different color from the first two.
Now, the total number of ways Jessie can choose and arrange the colors for the 3 rooms is given by multiplying the number of choices for each room:
\[
7 \text{ (for the first room)} \times 6 \text{ (for the second room)} \times 5 \text{ (for the third room)} = 7 \times 6 \times 5
\]
Calculating this:
\[
7 \times 6 = 42
\]
\[
42 \times 5 = 210
\]
Therefore, the total number of different ways Jessie can paint her rooms is \( \boxed{210} \).