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?

Question

Amara Patterson

Business

31 October, 09:26

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?

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Alena Maldonado · 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) !)