Final answer:
The number of different groups of three that can be formed from 12 recent graduates is 220, calculated using the combination formula C(n, k) = n! / (k!(n-k)!), with n=12 and k=3.
Step-by-step explanation:
The student has asked how many different groups of three can be selected from a pool of 12 recent graduates when a company has three positions open. This is a problem of combinations in mathematics because the order in which the graduates are chosen does not matter.
To determine the number of combinations, we use the combination formula:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial.
For this problem, n = 12 and k = 3.
So, C(12, 3) = 12! / (3!(12-3)!) = (12*11*10) / (3*2*1) = 220.
Therefore, the company can form 220 different groups of three from the 12 graduates.