Graduate Management Admission Test (GMAT) Practice Test

How many ways can 9 people be divided into 3 groups of 3?

1. 210

2. 280

3. 360

4. 450

The correct answer is: 280

To determine how many ways 9 people can be divided into 3 groups of 3, start by recognizing that the arrangement of the individuals into groups involves combinations and considering the arrangement of the groups themselves. First, select the first group of 3 from the 9 individuals. The number of ways to choose 3 people from 9 is calculated using the combination formula: \[ \binom{9}{3} = \frac{9!}{3!(9-3)!} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84 \] After selecting the first group, you have 6 individuals remaining. Now, select the second group of 3 from these 6. The number of ways to choose 3 from 6 is: \[ \binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20 \] This leaves you with 3 individuals for the final group, which can only be formed in 1 way, as all remaining individuals will