There are several ways to solve this question.

First, 15 members are interested in investment banking (IB) and 6 are NOT interested in IB

We want P(have at least 1 interested in IB)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(have at least 1 interested in IB) = 1 - P(not have at least 1 interested in IB)
What does it mean to not have at least 1 interested in IB? It means getting ZERO members interested in IB.
So, we can write: P(have at least 1 interested in IB) = 1 - P(have ZERO interested in IB)

Okay, let's go...
P(have ZERO interested in IB) = P(1st person is NOT interested in IB AND 2nd person is NOT interested in IB)
= P(1st person is NOT interested in IB) x P(2nd person is NOT interested in IB)
= 6/21 x 5/20
= 1/14


So, P(at least 1 interested in IB) = 1 - P(not at least 1 interested in IB)
= 1 - 1/14
= 13/14

Answer: E

Cheers,
Brent