Balanced Committee

Choose the women and men independently.

Use $\left(\genfrac{}{}{0ex}{}{6}{2}\right)\left(\genfrac{}{}{0ex}{}{5}{2}\right)$.

1. 1. Choose each group

   There are $\left(\genfrac{}{}{0ex}{}{6}{2}\right)$ choices for women and $\left(\genfrac{}{}{0ex}{}{5}{2}\right)$ choices for men.

2. 2. Multiply

   Independent selections multiply.

   $$\left(\genfrac{}{}{0ex}{}{6}{2}\right)\left(\genfrac{}{}{0ex}{}{5}{2}\right)=15\times 10=150$$

Answer: 150