Combinatorics Homework Help: 12 Workers, 4 Jobs, 277200 Solutions

[Norway]

Homework Statement

An IT-company with 12 hired workers, has been given four jobs. The company wants to use four workers on the first job, three on the second, three on the third and two on the last job. How many ways can the company put these 12 people on the four different jobs?

The answer's supposed to be 277 200.

The Attempt at a Solution

We've never ever done combinatorics like this, and the sole reason I'm doing this is because I'm ahead of the rest of my class. Still, I can't figure out how to figure out this problem. I've tried multiplying in different ways I know from probability math earlier, but with no luck. My guess is that matrixes(?) are needed here, but I've never done this before, so I really hope there are some kind ones around who can help me. :-)

Thanks a lot,
From Norway

 

[mjsd]

how many ways to pick 2 ppl out of 12 then how many ways to pick 3 from 10 then how many ways to pick 3 from 7, the remaining form the 4... multiply together to get answer

 

[Norway]

So it's something like ...
$${12 \choose 4} \cdot {8 \choose 3} \cdot {5 \choose 3} \cdot {2 \choose 2}$$
?
Thanks anyway :)

 

[mjsd]

should get same answer either way