Answer to Question #347905 in Statistics and Probability for Star

Question

In the class of Statistics, there are 75 students in total out of which 55 male, 20 female students. 10 students need to be selected for the occasion of freshers' reception.

a. What is the probability that 4 of the selected students would be girls?

Answer 1

We can select 10 students out of 75 in $C_{75}^{10}$ ways.

We can select 4 girls out of 20 in $C_{20}^{4}$ ways.

We can select 6 boys out of 55 in $C_{55}^{6}$ ways.

We can select 4 girls out of 20 and 6 boys out of 55 in $C_{20}^{4} \cdot C_{55}^{6}$ ways.

The probability that 4 of the selected students would be girls:

$P=\frac{C_{20}^{4} \cdot C_{55}^{6}}{C_{75}^{10}} \approx 0.1694=16.94\%.$

Answer: $\frac{C_{20}^{4} \cdot C_{55}^{6}}{C_{75}^{10}}$ (16.94%)