一个由24名学生组成的班级有11名女生 and 13名男生。为了组成班委会，随机挑选四名学生分别担任“班长”、“副班长”、“司库”和“秘书”。

1. Calculate the probability that all 4 selected committee members are girls.

$\mathrm{P}(\text{all girls}) = \frac{11}{24} \times \frac{10}{23} \times \frac{9}{22} \times \frac{8}{21} = \frac{5}{161}$

2. Calculate the probability that all 4 selected committee members are boys.

$\mathrm{P}(\text{all boys}) = \frac{13}{24} \times \frac{12}{23} \times \frac{11}{22} \times \frac{10}{21} = \frac{65}{966}$

3. Use the complement rule to find the probability of having at least one girl and at least one boy.

$\mathrm{P}(\text{at least 1 girl and 1 boy}) = 1 - \mathrm{P}(\text{all girls}) - \mathrm{P}(\text{all boys}) \\ = 1 - \frac{5}{161} - \frac{65}{966} \\ = 1 - \frac{30}{966} - \frac{65}{966} \\ = 1 - \frac{95}{966} = \frac{871}{966}$

1. Set up the probability expression for the two specific roles being filled by girls

Since the remaining two roles (Chairperson and Vice Chairperson) can be filled by anyone and do not restrict the Treasurer and Secretary positions, we can focus entirely on picking 2 girls from the class for these 2 specific roles.

$\text{P(Treasurer and Secretary are girls)} = \text{P(1st is a girl)} \times \text{P(2nd is a girl given 1st is a girl)}$
$= \frac{11}{24} \times \frac{10}{23}$

2. Evaluate and simplify the fraction