Good explanation needed for this one Jane has to pick 3

Here are 3 ways of looking at this:
(1)
WE are already given that E is chosen, so the problem is simply what is the prob that she will pick B if she chooses 2 subjects.

This is the probability that she will either choose the subject as the first pick OR the subject as the second pick.

Pr(b 1st) = 1/5
Pr(b 2nd) = Pr(b not 1st AND b 2nd) = 4/5 * 1/4 = 1/5

These 2 are mutually exclusive, hence the probability is 1/5 + 1/5 = 2/5 = 0.4

Method 2:
The probability that she will NOT leave B as one of her 3 unpicked choice is exactly the same problem.
Pr(B is NOT one of 3 unpicked choices) = 4/5 * 3/4 * 3/2 = 2/5 = 0.4

Method 3:
Pr (b picked in 2 choices) = 1 - Pr(B not picked of her two choices)
= 1 - (4/5 * 3/4) = 1 - 3/5 = 2/5 = 0.4.