75 employees total, 25 per store, what are the chances the 3 lowest performance scores would be 1 employee from each store?

Question

3 stores.

25 employees each.

All 75 employees ranked from highest to lowest with some employees having equal ratings.

What are the chances that the 3 lowest ranked employees would be one employee from each store?

Answer 1

There are (75 choose 3) = 67525 total ways to choose 3 employees to be the lowest performers.

 

There are (25 choose 1) = 25 ways to choose 1 employee from a single store. So, there are 25×25×25 = 15625 ways to choose one employee from each store.

 

That's a probability of:

 

(successes)/(total) = 15625/67525 = 0.231