If exactly 2 trucks were sent to city A ,and exactly 4 trucks for city B and exactly 1 truck for city C

here is my thought process ,i looked at city C first and said there is 7 different possibilities ,then i looked at A and said to my self there is C(6,2) different possibilities ,and then only C(4,4) for B.
so the final count should be 7\*C(6,2)\*C(4,4) ,is this correct?
if not can you advise me on how to approach these kind of problems?;
i'm new to combinatorics.