A quiz team of 4 is to be picked from 5 boys and 4 girls. The team must include at least 2 girls. How many different teams are possible?

Explanation

1. 01

   Split into cases by the number of girls.

2. 02

   2 girls: ${}^{4}C_{2} \times {}^{5}C_{2} = 6 \times 10 = 60$. 3 girls: ${}^{4}C_{3} \times {}^{5}C_{1} = 4 \times 5 = 20$. 4 girls: ${}^{4}C_{4} = 1$.

3. 03

   Teams $= 60 + 20 + 1 = 81$.

4. 04

   Check: total teams ${}^{9}C_{4} = 126$, minus 5 with no girl and 40 with one girl, gives 81.