Out of 90 applicants for a job, 60 people get selected after the interview. If five applicants are selected at random,calculate the probability that 2 will get selected.

To calculate the probability, we need to find two quantities:

1. The total number of ways to choose 5 applicants out of 90.
2. The total number of ways to choose 2 applicants out of the 60 selected.

Let's calculate these two quantities one by one:

1. Total number of ways to choose 5 applicants out of 90:
We can use the combination formula, which is given by: nCr = n! / (r!(n-r)!)
Here, n = 90 (total number of applicants) and r = 5 (number of applicants to be chosen).
So, the number of ways to choose 5 applicants out of 90 = 90! / (5!(90-5)!) = (90! / (5!85!))

2. Total number of ways to choose 2 applicants out of 60 selected:
Similarly, using the combination formula, here n = 60 (total number of selected applicants) and r = 2 (number of applicants to be chosen).
So, the number of ways to choose 2 applicants out of 60 = 60! / (2!(60-2)!) = (60! / (2!58!))

Now, to find the probability of 2 out of 5 applicants getting selected, we divide the second quantity by the first quantity:

Probability of 2 out of 5 applicants getting selected = (60! / (2!58!)) / (90! / (5!85!))

Simplifying this expression will yield the final probability.

Note: The factorial of a number n, denoted as n!, is the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.