The problem is:

A pianist wants to prepare a recital that will consist of 3 Classical, 4 Romantic and 2 Contemporary pieces.

In how many ways can he order the piano pieces if he wants to play all the pieces of a genre together?

I'm a bit confused with these kind of problems, when the first choice could influence a second choice. If the first choice would be a Classical piece, then the following pieces must be Classical as well. Anyway, my reasoning was as follows, using the fundamental counting principle:

In total there are 9 "events (E's)", because there are 9 pieces of music in total.

E1 =9choices

E2 =2choices, if for example, the first choice (E1) was a Classical piece

E3 = then must be another Classical piece which is1remaining choice

E4 =6choices (4R + 2C)

E5 = if Romantic was chosen at E4, then here are3choices

E6 =2choices

E7 =1choice

E8 =2choices, only Contemporary left

E9 =1choice

So the total number of ways this can happen is: 9*2*1*6*3*2*1*2*1 =1260 ways.

According to the answer sheet this is incorrect. The correct answer should be1728 ways.

Can somebody show me where my reasoning if faulty?