GMAT Quantitative Reasoning Practice Test 4

The basic principle of this question is that one person can’t be elected to more than one part, therefore when picking a person for a job the “inventory” of remaining people is growing smaller. The probability of picking a girl for the first job is $\frac{4}{10}=\frac{2}{5}$.
The probability of picking a girl for the second job is $\frac{\left(4-1\right)}{\left(10-1\right)}=\frac{3}{9}$.
The probability of picking a girl for the third job is $\frac{\left(3-1\right)}{\left(9-1\right)}=\frac{1}{4}$.
The probability of all three events happening is: $\frac{2}{5}\times \frac{3}{9}\times \frac{1}{4}=\frac{1}{30}$.