In a class of 15 students, 5 of them are boys and 10 students are girls. A team of 11 members has to be formed at random. The probability that the, team has at least 4 boys, is  

A team of 11 members has to be formed from a class of 15 students

n(S)=${ }^{15}{C}_{11}$

E=Selecting at least  4 boys=4 boys and 7 girls ,5 boys and 6 girls

n(E)=${ }^5{C}_4{\times }^{10}{C}_7{+}^5{C}_5{\times }^{10}{C}_6$

Required probability  

$=\frac{{ }^5{C}_4{\times }^{10}{C}_7{+}^5{C}_5{\times }^{10}{C}_6}{{ }^{15}{C}_{11}}=\frac{600+210}{1365}=\frac{54}{91}$