# Assume that you have a total of 9 people on the board: 3 out-of-state seniors, 1 in-state senior, 2 out-of-state non-seniors, and 3 in-state non-seniors. University rules require that at least one in-state student and at least one senior hold one of the three offices. Note that if individuals change offices, then a different selection exists.In how many ways can the officers be chosen while still conforming to University rules?

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Assume that you have a total of 9 people on the board: 3 out-of-state seniors, 1 in-state senior, 2 out-of-state non-seniors, and 3 in-state non-seniors. University rules require that at least one in-state student and at least one senior hold one of the three offices. Note that if individuals change offices, then a different selection exists.

In how many ways can the officers be chosen while still conforming to University rules?

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Step 1

To work out the number of selections under the given conditions

Step 2

Out of these 9, 3 people are selected  for the three offices A, B and C with the given constraints

Step 3

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