Final answer:
To find the number of different ways to select 3 students from a group of 9, we use the combinations formula: C(9, 3) = 9! / (3!6!) = 84. Thus, the college can make 84 different groups of three students for the assistantships.
Step-by-step explanation:
The question asks us to determine the number of different ways to select 3 students from a group of 9 for graduate assistantships. This is a problem related to combinations, which is a part of mathematics known as combinatorics. Since the order in which the assistantships are awarded does not matter, we want to find the number of combinations of 9 students taken 3 at a time, often notated as C(9, 3) or 9 choose 3.
To calculate this, we can use the combinations formula:
C(n, k) = \( \frac{n!}{k!(n-k)!} \)
Where n represents the total number of items, k represents the number of items to choose, and '!' denotes the factorial operation. Applying the formula:
C(9, 3) = \( \frac{9!}{3!(9-3)!} \) = \( \frac{9!}{3!6!} \) = \( \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \) = 84
Therefore, the college can make 84 different groups of three students for the assistantships.