91Ó°ÊÓ

Total mathematics students=100

The students are divided into five classes, each containing 20 students. And, the awards are to be given to 10 students.

To choose 10 students from 100 mathematics students, there are\(^{100}{C_{10}}\)ways.

To choose 2 from 20 students (for each of the 5 classes), there are\(^{20}{C_2}\)ways.

Therefore, to choose two students from each class, there are\({\left( {^{20}{C_2}} \right)^5}\)ways.

All outcomes are equally likely, hence the probability is,

\(\begin{aligned}{}{\rm{P}} &= \frac{{{{\left( {^{20}{C_2}} \right)}^5}}}{{\left( {^{100}{C_{10}}} \right)}}\\ &= \frac{{{{\left( {190} \right)}^5}}}{{\left( {^{100}{C_{10}}} \right)}}\\ &= \frac{{{{\left( {190} \right)}^5} \times 10! \times 90!}}{{100!}}\\ &= 0.143\end{aligned}\)

Thus, the required probability is 0.143.