Probability and how to solve word problem

Question

a 4 person committee consisting of parents and teachers is to be selected from 14 parents and 4 teachers. Find the probability of selecting 2 parents and 2 teachers.

Answer 1

The probability of drawing just one teacher is $\frac{4}{18}$

The probability of drawing just one parent is $\frac{14}{18}$

There are $\frac{4!}{2!21} = 6$ possible orders in which you could draw two teachers and two parents.

TTPP TPTP PTPT PPTT TPPT PTTP

The probability of drawing two teachers and two students in a the order TTPP is: $\frac{14}{18} \frac{13}{17} \frac{4}{16}\frac{3}{15}$

This is the same probability for the other five possible orders.

Thus the final answer is $6 \times \frac{14}{18} \frac{13}{17} \frac{4}{16}\frac{3}{15}$