Question

@Mathematics 3 students are selected at random from a class consisting of 5 freshman, 3 sophomores, and 2 juniors. Find the probability that 2 freshman and 1 junior are selected given that at least 1 freshman is selected.

Answer 1

good problem, reminds me of my school days

Answer 2

axiomatic way is better, what it asks is
\[P(F= 2 , J = 1 | F \geq 1)\]
which is same as
\[P(F = 2, J =1 , F \geq 1)/P(F \geq 1)\]
\[= \frac{P(F = 2, J =1)}{P(F = 1 ) + P(F =2) + P(F=3)}\]
Now find the probabilities in the following way:
\[P(F = 2, J = 1) = P(J =1)P(F = 2 |J = 1) = \frac{2}{10} \cdot \frac{5}{9} \cdot \frac{4}{8}\]

and so on. Hope this helps