Committee from officers and jawans (at least one officer): From 4 officers and 8 jawans, how many 6-person committees include at least one officer?

Introduction / Context:We must count 6-person committees that include at least one officer. The complement (no officer) is easier to compute and subtract from the total committees possible.

Given Data / Assumptions:Total people = 12 (4 officers + 8 jawans); committee size = 6.

Concept / Approach:Total − (no officer). No-officer committees must be formed entirely from jawans.

Step-by-Step Solution:

Verification / Alternative check:Summing by officer count (1 to 4) reproduces 896.

Why Other Options Are Wrong:986, 886, 996 are off by ignoring the complement or miscomputing combinations.

Common Pitfalls:Accidentally allowing 0 officers; arithmetic slips on C(12,6) or C(8,6).

Final Answer:896