Dominate the GMAT 2026 – Turbo Charge Your Business School Dreams!

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