**Topic**

Class 10A has 16 boys and 24 girls. Randomly select 5 friends to assign daily. Find the probability of event A “Out of the 5 chosen students, there are 2 boys and 3 girls”

**Solution method – See details**

The probability of event A being a number, symbol \(P\left( A \right)\) is determined by the formula: \(P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( \Omega \right)}}\), where \(n\left( A \right)\) and \(n\left( \Omega \right)\) denote the number of elements of set A and \(\Omega \) respectively.

**Detailed explanation**

+ Each way choose 5 students from 40 students \( \Rightarrow n\left( \Omega \right) = C_{40}^5\)

+ Choose 2 boys and 3 girls \( \Rightarrow n\left( A \right) = C_{16}^2.C_{24}^3\)

\( \Rightarrow P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( \Omega \right)}} = \frac{{C_{16}^ 2.C_{24}^3}}{{C_{40}^5}} = \frac{{10120}}{{27417}}\)