A committee is to be formed from $4$ men and $6$ women such that it includes at least $2$ men and exactly twice as many women as men. The number of such committees is:
Step-by-Step Solution
Key Concept: Let $m$ men, $2m$ women, $m \geq 2$. Available: $\leq 4$ men, $\leq 6$ women. $m = 2$: $\binom{4}{2}\binom{6}{4} = 6 \times 15 = 90$. $m = 3$: $\binom{4}{3}\binom{6}{6} = 4 \times 1 = 4$. $m = 4$ needs 8 women — impossible. Total $= 94$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)