Question

Jean Paul is an interior designer who is working with a difficult client. Part of his design requires that he put 11 colored vases in a row on a shelf. He has 3 identical blue vases, 2 identical green vases, 4 identical red vases, a purple vase and a yellow vase. He has put up 4 different arrangements of the vases that his client complained about. As he begins to put up the fifth arrangement, he wonders how many different arrangements he might have to go through before his client complains about all of them. How many different arrangements could Jean Paul make

Answer 1

138600 arrangements

Explanation:

Let n = 11

The different arrangements Jean Paul can make = n!/(4!)(3!)(2!)

Hence, 11!/(4!)(3!)(2!) = 1663200/12 = 138600