Here, to find the denominator what’s wrong with calculating it like:
JJS = 3 x 2 x 3 = 18
JSS = 3 x 3 x 2 = 18
Total = 36
and while calculating the num by brute force i’m getting 12 and not 9.
Can anyone check this?
This calculation considers the order in which the students are picked. In the context of the question, we don’t care about the order.
For example,
{A,B,C} are juniors and {D,E,F} are seniors.
Your calculation counts ( A, B, D) and (B, A, D) twice, while it should have been counted only once.
Can you share your brute force approach?
You’ve correctly identified that there are 20 cases total. Now remove 1 case for all juniors and another for all seniors.
In the remaining 18 cases it will be 9 cases for 1 J + 2 S, and 9 for 2 J + 1 S.
In the 1 J + 2 S case its a 1/3 probability that Jane is there hence 3 cases here
In the 2 J + 1 S case its a 2/3 probability that Jane is either of the juniors hence 6 cases.
Total = 9 cases.