Probabilty Question

Question

A university's leadership council is made up of members: are students, are teachers, and are deans. A newspaper reporter is planning to select two of the council members for interviews. The first member will be chosen at random, and then the second member will be chosen at random from the remaining members. What is the probability that two students will be selected?

Answer 1

say for example

there were 3 students, 4 teachers, 2 deans

s=3, t=4, d=2

chance of 2 students = 3/(3+4+2) x 2/8 x 2 = 3/9 x 1/4 = 1/3x 1/4 = 1/12

chance o 2 teachers = 4/9 x 3/8 = 1/6

chance of 2 deans = 2/9 x 1/8 = 1/36

chance of 1 student & 1 teacher = 1/3 x 4/8 x 2 = 1/6 x 2 = 1/3

chance of 1 student & 1 dean = 1/3 x 2/8 x 2 = 1/12 x 2 = 1/6

chance of 1 teacher and 1 dean = 4/9 x 2/8 x2 = 1/9 x 2 = 2/9

sum = 2/9 +1/6+1/3 +1/36 +1/6 + 1/12

= (8+6+12+1+6+3)/36 = 36/36 = 1

sum of all outcome's probabilities = 1 = 100%