## Solving Lesson 33 Page 48 Math Workbook 10 – Kite>

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 $$\Rightarrow n\left( A \right) = C_{16}^2.C_{24}^3$$

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