Problem
COM-B1-M03-P023 Team with Minimums
#23
★★★★☆ Level 4 of 5
From \(8\) boys and \(7\) girls, a team of \(6\) is chosen. How many teams have at least \(2\) boys and at least \(2\) girls?
Split by the number of boys: \(2,3,4\).
The possibilities are \(2\) boys and \(4\) girls, \(3\) and \(3\), \(4\) and \(2\). We get \(\binom{8}{2}\binom{7}{4}+\binom{8}{3}\binom{7}{3}+\binom{8}{4}\binom{7}{2}=28\cdot35+56\cdot35+70\cdot21=4410\).
Strong problem on careful cases.