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How many ways can a group of 9 politicians be divided into committees that contain groups of 4, 3, and 2 politicians per committee?

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Final answer:

There are 1260 ways to divide the group of 9 politicians into committees with groups of 4, 3, and 2 politicians per committee.

Step-by-step explanation:

To divide a group of 9 politicians into committees with groups of 4, 3, and 2 politicians per committee, we can use a combination of combinatorics and permutations.

First, let's calculate the number of ways we can choose 4 politicians out of the 9. This can be done using the combination formula C(9, 4) = 9! / (4! * (9-4)!), which simplifies to 126 ways.

Next, we have 5 politicians remaining to form the next committee of 3. Using the same combination formula, we can calculate C(5, 3) = 5! / (3! * (5-3)!), which simplifies to 10 ways.

Finally, we have 2 politicians left to form the last committee of 2. Again, using the combination formula, we can calculate C(2, 2) = 2! / (2! * (2-2)!), which simplifies to 1 way.

To calculate the total number of ways, we multiply the number of ways for each committee: 126 * 10 * 1 = 1260 ways.

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