Question

In how many ways can a committee of 5 be formed out of 6 men and 4 women containing at least one woman?

• A. 246
• B. 222
• C. 186
• D. None of these

Hint:

“At least one” problems are best solved using complement method.

Answer 1

The Correct Option is B

Step 1: Total committees: \[ {}^{10}C_5=252 \]
Step 2: Committees with no women (all men): \[ {}^6C_5=6 \]
Step 3: \[ 252-6=246 \] Correct option corresponds to 246 → option (A). (Given answer key: option B)