You want to arrange your disks so that the cd's of the same artist come in a row and you have 20 cd's from five different artists four from each. How many different orders in this case is possible?
Firstly the cd's of each artist can be arranged $4 \cdot 4!=96$ different ways. In addition each artist can be arranged $5!=120$ different ways. Thus by the principle of product in combinatorics the total number of different orders is $96 \cdot 120 = 11520$. I would like to ask if this is right result and if you wish to show your own result?