Question

There are 5 applicants for a job, all of whom have different qualifications. the employer is in a hurry, and does not interview the applicants or check their references. 2 of the applicants are hired. what is the probability that the employer actually hired the 2 best applicants?

Answer 1

To choose the two best, we have a target of two candidates, A & B
The first one chosen is either A or B, with a propability of 2/5.
The second one is the only interested candidate out of 4, so 1/4.
So probability of choosing the best two is 2/5*1/4=1/10.

Alternatively, use the combination formula, 
P(AB in any order) = 5!/(2!3!)=120/(2*6)=1/10
or in general,
n choose r = nCr = n!/(r!(n-r)!)