There are two imposters and seven crewmates on the rocket ‘Plus’. How many ways are there for the nine people to split into three groups of three, such that each group has at least two crewmates? The two imposters and seven crewmates are all distinguishable from each other, but we’re not concerned with the order of the three groups.
For example: \(\{I1,C1,C2\}\), \(\{I2,C3,C4\}\) and \(\{C5,C6,C7\}\) is the same as
\(\{C3,C4,I2\}\), \(\{C5,C6,C7\}\) and \(\{I1,C2,C1\}\) but different from
\(\{I2,C1,C2\}\), \(\{I1,C3,C4\}\) and \(\{C5,C6,C7\}\).