What is the probability of the two aspirants? A company needs to fill two jobs and fifty aspirants are presented. Thirty of the applicants are affiliated and the rest are not. If two people are chosen at random, calculate the probability that:


*

*None of the chosen is affiliated,

*one of the two is affiliated,

*the two are affiliated


My Solution:
Total of aspirants=50
Aspirants with affiliation=30
Aspirants without affiliation=20


*

*P=$\frac{\binom{20}{2}}{\binom{50}{2}}=0.1551$

*P=$\frac{\binom{30}{1}+\binom{20}{1}}{\binom{50}{2}}=0.04081$

*P=$\frac{\binom{30}{2}}{\binom{50}{2}}=0.3551$
Is my solution correct?

Given that these are the only 3 possible oucomes, their probabilities should add up to 1, and they don't, so you can immediately tell something is wrong.
Here is what is wrong:
In 2. you should multiply $30\choose1$ and $20\choose1$ in the numerator.
