Question

A museum curator is hanging 9 paintings in a row for an exhibit. There are 6 Renaissance paintings and 3 Baroque paintings. From left to right, all of the Renaissance paintings will be hung first, followed by all of the Baroque paintings. How many ways are there to hang the paintings?

Answer 1

4,320ways

Explanation:

We are given the following from the questions

Number of paintings = 9

Renaissance paintings= 6

Baroque paintings = 3

Since they are hanging from left to right and we will first hang Renaissance painting before baroque painting, hence;

For Renaissance painting, this can be done in 6! ways

6! = 6*5*4*3*2*1

6! = 720ways

Similarly for Baroque painting, this can be done in 3! ways

3! = 3*2*1

3! = 6ways

The total number of ways to hang the painting = 6!*3!

The total number of ways to hang the painting = 720 * 6

The total number of ways to hang the painting = 4,320ways

Hence there are 4,320ways to hang the paintings