So, the question is, 

"In how many ways can 6 persons be selected from 4 officers and 8 constables if at least one officer is to be included?"

I did this,

*4C1 x 11C5*

I first selected one officer from the 4 officers and then selected remaining 5 from the 11 persons remaining. 

The answer I'm getting is wrong, the correct one is 896 which I got by subtracting the total number of combinations by using only constables minus all the combinations, 

*12C6 - 8C6*

It would be great if someone can point out the mistake I committed in my first logic.

Thanks!