A group of students comprises of 5 boys and n girls. If the number of ways in which a team of 3 students be selected from this group such that there is atleast one boy and atleast one girl in each team is 1750 then n is

${ }^{(n+5)}{C}_3{-}^5{C}_3{-}^n{C}_3=1750$

$\Rightarrow n^2+3n-700=0\Rightarrow n=25\left(\text{ or }\right)-28$

or

$$\begin{gathered} 5\text{ boys and }\mathrm{n}\text{ girls } \\ \text{ Number of ways of selecting a team with }1\text{ boy and }2\text{ girls }{=}^5{\mathrm{C}}_1{\cdot }^{\mathrm{n}}{\mathrm{C}}_2 \\ \text{ Number of ways of selecting a team with }2\text{ boy and }1\text{ girls }{=}^5{\mathrm{C}}_2{\cdot }^{\mathrm{n}}{\mathrm{C}}_1 \\ \begin{array}{r}{ }^5{\mathrm{C}}_1{\cdot }^{\mathrm{n}}{\mathrm{C}}_2{+}^5{\mathrm{C}}_2{\cdot }^{\mathrm{n}}{\mathrm{C}}_1=1750\\ 5\cdot \frac{\mathrm{n}(\mathrm{n}-1)}{2!}+10\cdot \mathrm{n}=1750\\ {\mathrm{n}}^2+3\mathrm{n}=700\end{array} \\ \begin{array}{l}\Rightarrow {\mathrm{n}}^2+3\mathrm{n}-700=0\\ \Rightarrow {\mathrm{n}}^2+28\mathrm{n}-25\mathrm{n}-700=0\\ \Rightarrow (\mathrm{n}-25)(\mathrm{n}+28)=0\\ \Rightarrow \mathrm{n}=25\text{ or }\mathrm{n}=-28\\ \therefore \boxed{\mathrm{n}=25.}\end{array} \end{gathered}$$