Problem
COM-B1-M03-P007 At Least Two Girls
#7
★★☆☆☆ Level 2 of 5
From \(5\) girls and \(4\) boys, a team of \(4\) is chosen. How many teams contain at least two girls?
Split into \(2,3,4\) girls.
We get \(\binom{5}{2}\binom{4}{2}+\binom{5}{3}\binom{4}{1}+\binom{5}{4}=10\cdot6+10\cdot4+5=105\).
First casework by team composition.