First choose 2/9 civilians * choose 2/5 officers * the remaining
= 9C2 * 5C2 * (7+3)
= (9 * 8)/2 * (5*4)/2 * 10
No. In your approach you are triple couting all the options. So you need to divide by 3 to get the correct answer.
Let us say m1-m5 are the 5 military guys and c1-c9 are the 9 civvis. In your expression,m1 m2 + c1 c2 + m3
group is counted as being different from m1 m3 + c1 c2 + m2
and m2 m3 + c1 c2 + m1[/
. In actuality they are all same m1m2m3 and c1c2
So for each case you are taking 3 cases. Divide by 3 adn you will get the right answer.