Jessie's apartment has 3 rooms. She will paint each room a different color. She is choosing between 7 different paint colors.

Question

In how many different ways can Jessie paint her rooms? Enter the answer in the box.

Response area with 1 text input box
different ways

Answer 1

To determine how many different ways Jessie can paint her 3 rooms using 7 different colors, we can use the concept of permutations, since the order in which the rooms are painted (different colors for each room) matters, and she cannot use the same color for more than one room.

1. For the first room, she has 7 color options.
2. For the second room, since one color has already been used, she has 6 remaining options.
3. For the third room, with two colors already used, she has 5 options left.

The total number of different ways Jessie can paint her 3 rooms is calculated by multiplying the number of choices for each room:

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

So, there are 210 different ways Jessie can paint her rooms.