Hello, jzellt!

I assume that the 100 CD's are distinguishableThere is a CD player that holds 5 CDs.

There are 5 trays that hold one CD each. I have 100 CD's.

In how many ways can the CD player be loaded if AT MOST two CD's are placed in it?

. . and that the 5 trays are also distinguishable.

Place one CD into the player.

There are 100 choices for the CD.

There are 5 choices for the tray to place it in.

. . There are: . ways to load one CD into the player.

Place two CD's into the player.

There are ways to choose two CD's.

There are: . ways to place them in the trays.

. . There are: . ways to load two CD's into the player.

Therefore, there are: . ways to load at most two CD's.