In how many ways can a child arrange 5 identical red blocks

In how many ways can a child arrange 5 identical red blocks, 3 identical blue blocks and 6 identical green blocks in a row?

Solution

If the condition is to place each color at as one set , it will be 5!*3!*6!*3! = 3110400 ways. because each color set could be change inside of set, for example 5 identical red blocks are arranged in 5! ways. and the last 3! will be the arrangements of 3 sets red,blue,green

if the condition is to place all the blocks identical it 14! are the ways to arrangement = 87178291200