A class consists of 80 students,25 of them are girls and 55 are boys. If 10 of them are rich and the remaining are poor and also 20 of them are intelligent, then the probability of selecting an intelligent rich girl is

Total number of the students is 80. 

A student is selected$\Rightarrow n\left(S\right)=80$

Total number of girls is 25. Total number of boys is 55. There are 10 rich, 70 poor, 20 intelligent students in the class.

A=Selecting an intelligent student

B=Selecting  a rich student 

C=Selecting a girl student

$$\begin{gathered} P\left(A\right)=\frac{20}{80}=\frac{1}{4},P\left(B\right)=\frac{10}{80}=\frac{1}{8},P\left(C\right)=\frac{25}{80} \\ A,B,C are independent \\ P(A\cap B\cap C)=P\left(A\right)P\left(B\right)P\left(C\right)=\frac{1}{4}\times \frac{1}{8}\times \frac{25}{80}=\frac{5}{512} \end{gathered}$$