Question

The number of ways in which we can choose a committee from 3 men and 6 women so that the committee includes at least two men and exactly twice as many women as men is

• A. 35
• B. 42
• C. 46
• D. 52
• E. 55

Hint:

Translate word conditions into equations before solving.

Answer 1

The Correct Option is C

Concept: Use combinations with conditions.

Step 1: Let men = $m$, women = $2m$
At least 2 men $\Rightarrow$ $m=2$ or $3$

Step 2: Check possibilities
For $m=2$: women = 4 Ways: \[ \binom{3}{2}\binom{6}{4} = 3 \times 15 = 45 \] For $m=3$: women = 6 Ways: \[ \binom{3}{3}\binom{6}{6} = 1 \]

Step 3: Total
\[ 45 + 1 = 46 \] Final Conclusion:
Option (C)