Given nine different English books, seven different French books, and five different German books.

How many ways are there to make a row of three books in which exactly one language is missing (the order of the three books makes a difference)?

The answer is

3*[9*8* (7+5) + 7*6*(9+5) + 5*4*(9+7)]

I do not understand how to get there.

I have 3 locations in the row _ _ _

In the case I use only French and German books I have

7+5=12 books availabe to place

I do not kow where the 9*8 come from in the expression 3*(9*8*(7+5))

I seem to have 3 subsets which are added (French/German, Engl/German, Engl/French).

Can someone help me out? Thanks