quantitative question about combination :s

Hi everyone, I already posted my question on one topic but i had no answer.. i would be really grateful if someone would make me understand.

here is the question : a-group-consists-of-5-officers-and-9-civilians-if-you-must-91779.html
"A group consists of 5 officers and 9 civilians. If you must select a committee of 5 people, and the committee must include at least 2 officers and at least 2 civilians, how many different committees are possible?"

and here is the answer :

To meet the conditions we can have only 2 cases:
2 officers and 3 civilians: \(C^2_5*C^3_9=840\);
3 officers and 2 civilians: \(C^3_5*C^2_9=360\);

Total: 840+360=1,200.

so 3600 +1200 = 4800

but the thing I don't get is why we don't divide \(C^2_5*C^3_9\) and \(C^3_5*C^2_9\) by 2! as it is explain in this question? six-highschool-boys-gather-at-the-gym-for-a-modified-game-161915.html

where it is explained : when we make a combination and we don't want to order, we divide by n!

please help