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.

Answer 1

To determine how many different ways Jessie can paint her 3 rooms with 7 different colors, where each room is painted a different color, we can use the concept of permutations since the order in which the colors are assigned to the rooms matters.

1. **Choose a color for the first room:** There are 7 available colors.
2. **Choose a color for the second room:** After painting the first room, 6 colors are left to choose from.
3. **Choose a color for the third room:** After painting the first two rooms, 5 colors remain.

Therefore, the total number of ways to paint the rooms can be calculated as follows:

\[
7 \times 6 \times 5
\]

Calculating this gives:

\[
7 \times 6 = 42
\]
\[
42 \times 5 = 210
\]

Thus, the total number of different ways Jessie can paint her 3 rooms is

\[
\boxed{210}
\]