A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) at least three girls.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) at least three girls.

Solution:

It is known that

${ }^{n} C_{r}$ $=\frac{n !}{r !(n-r) !}$

(i) At least three girls

The total no. of ways in which the team can have at least three girls $={ }^{4} \mathrm{C}_{3}{ }^{7} \mathrm{C}_{2}+{ }^{4} \mathrm{C}_{4}{ }^{7} \mathrm{C}_{1}$

$\begin{array}{l}
=4 \times 21+7 \\
=84+7 \\
=91
\end{array}$