Problem
COM-B1-M03-P017 More Boys Than Girls
#17
★★★☆☆ Level 3 of 5
From \(6\) boys and \(5\) girls, a team of \(5\) is chosen. How many teams have more boys than girls?
Possible numbers of boys are \(3,4,5\).
Cases: \(3\) boys and \(2\) girls: \(\binom{6}{3}\binom{5}{2}=200\); \(4\) boys and \(1\) girl: \(\binom{6}{4}\binom{5}{1}=75\); \(5\) boys: \(\binom{6}{5}=6\). Total: \(281\).
Inequality condition becomes cases.