Question

There are 10 Boys and 5 Girls in a class. Three students are chosen at Random one after the other. Find the probability that 1. First two are boys and third is girls. 2. First two are girls and third is boy

Answer 1

$Boys = 10$

$Girls =5$

$Total= 15$

Let the total number of boys be 'b', and number of girls be 'g' and the total number of persons in the group be 'N'

From N, let the number of people selected be 'n' where a number 'x' is picked from boys (b) while a number'y' are picked from girls (g)

solution 1: 1st 2 are boys and 3rd girl

2 boys are picked from a group of 10 and 1 girl picked from a group of 5. In total, 3 people are picked from a group of 15

$$=\frac{_bC_x* _gC_y}{_N C_n}$$ $$\frac{10C_2* 5C_1}{15C_5}$$

answer: 0.0749

solution 2: 1st 2 are girls and 3rd boy

$$=\frac{5C_2*10C_1}{15C_5}$$

answer: 0.0333