From 4 officers and 8 jawans, the number of ways to choose 6 persons. so, as to include at least one officer is equal to 

Total Number of ways =   no of ways  chosing 6 persons from 4 officers and 8 jawans - no of ways of chosing 6 persons from 8 jawans

= ${ }^{12}{C}_6-{ }^8{C}_6=\frac{12!}{6!6!}-\frac{8!}{6!2!}=896$