Answer in the back of the book wrong?

Can someone please verify my answer? Because I'm sure I'm doing this question right but the answer at the back differs.

Q: A bridge hand consists of 13 cards. How many bridge hands include 5 of one suit, 6 cards of a second, and 2 cards of a third?

Isn't the solution: 13C5 x 13C6 x 13c2 = 172262376?

The answer at the back is 4134297024

EDIT:

Oh I just realized that I have to account for the fact that only 3 of the 4 suits are being utilized. And order is important so do I multiply the 172 262 376 by 4P3?