A Company short lists 40 applicant for an interview out of which 28 are men. If there are only five vacant posts to be filled, find the probability that the list of successful applicant contains at least 14 men

This problem can be solved using the concept of combinations and probability. Here are the steps:

1. Total number of ways to select 5 applicants from 40 is given by the combination formula C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, and r is the number of items to choose. So, total ways = C(40, 5).

2. Now, we need to find the ways to select at least 14 men. This means we can have 14, 15, 16, ..., 28 men. But since we only have 5 posts, the maximum number of men we can have is 5. So, we only need to consider the case of 5 men.

3. The number of ways to select 5 men from 28 is given by C(28, 5).

4. The probability is then given by the number of favorable outcomes (ways to select 5 men) divided by the total number of outcomes (ways to select 5 applicants). So, Probability = C(28, 5) / C(40, 5).

5. Calculate the values to get the final probability.

This problem can be solved using the concept of combinations and probability. Here are the steps:

1. Total number of ways to select 5 applicants out of 40 is given by the combination formula C(n, r) = n! / [(n-r)! * r!] where n is the total number of items, and r is the number of items to choose. So, total ways = C(40, 5).

2. Now, we need to find the number of ways to select at least 14 men. This means we can have 14, 15, 16, ..., 28 men. But since we only have 5 posts, the maximum number of men we can have is 5. So, we only need to consider the case where all 5 selected are men. The number of ways to select 5 men out of 28 is given by C(28, 5).

3. The probability is then given by the number of favorable outcomes (selecting 5 men) divided by the total number of outcomes (selecting any 5 applicants). So, Probability = C(28, 5) / C(40, 5).

4. Calculate the values using the combination formula and simplify to get the final probability.