Question

The director of a government agency has been given a list of 12 firms cited for unfair labor practices. Because of staff shortage and inefficiency, only one-fourth of these 12 can be charged. How many possible sets of 3 firms can be charged?

Answer 1

220 sets

Explanation:

This is a combinations question - we don't care in which order we pick the 3 firms (picking firms A, B, C is the same as picking firms C, B, A). And so we can solve this with the combinations formula, the general formula of which is:

`C_(n,k)=(n!)/((k)!(n-k)!)` with `n="population", k="picks"`

`C_(12,3)=(12!)/((3)!(12-3)!)=(12!)/((3!)(9!))=>`

`(cancel12^2xx11xx10xxcancel(9!))/(cancel(3xx2)xxcancel(9!))=>`

`2xx11xx10=220`