Question

A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected is the team has at least $3$ girls ?

Answer 1

Total number of girls in the group $=4$

Total number of boys in the group $=7$

Probability of selecting atleast $3$ girls =?

By considering following ways we can select:

i) $3$ girls $+2$ boys $\Rightarrow {}^4{C}_3\times {}^7{C}_2$

ii) $4$ girls $+1$ boys $\Rightarrow {}^4{C}_4\times {}^7{C}_1$

Total number of ways $=({}^4{C}_3\times {}^7{C}_2)+({}^4{C}_4\times {}^7{C}_1)$

$=84+7$

$=91$