Find the number of ways to fill a box with a dozen doughnuts chosen from five

varieties, with the requirement that at least one doughnut of each variety is

picked.

Here is how I think this is done, is this correct?

1. Put one donut of each type in the box. 7 Donuts now left.

2. These donuts can be divided using the | and * method. So *******|||| stands for 7 donuts and 4 separators for the varieties, 11 items in total. The dividers can be placed in 11 Choose 4 = 330 ways.

Is this correct?