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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Asked Sep 13, 2019
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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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Expert Answer

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

3 out of state seniors(non-students)
in state seniors(non-students)
2 out of state students
3 in state students
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3 out of state seniors(non-students) in state seniors(non-students) 2 out of state students 3 in state students

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Step 3
number of selections
l)one in state student = 3
2)one senior = 3+1 4
the remaining office can be filled
in 7 ways
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number of selections l)one in state student = 3 2)one senior = 3+1 4 the remaining office can be filled in 7 ways

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