Number of permutations when composing recital

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 = **9** choices

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

E3 = then must be another Classical piece which is** 1** remaining choice

E4 = **6** choices (4R + 2C)

E5 = if Romantic was chosen at E4, then here are **3** choices

E6 = **2** choices

E7 = **1** choice

E8 = **2** choices, only Contemporary left

E9 = **1 **choice

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 be **1728 ways.**

Can somebody show me where my reasoning if faulty?

Re: Number of permutations when composing recital

Magically after writing my problem I think I found the right reasoning.

You can order the Classical pieces in 3*2*1 = 6 ways

The Romantic pieces in 4*3*2*1 = 24 ways

The Contemporary pieces in 2*1 = 2 ways

You can order the genres in 3*2*1 = 6 ways

Total number of ways = 6*24*2*6 = **1728 ways**

Right!? :P

Re: Number of permutations when composing recital