test4a.pdf - PLEASE READ THE FOLLOWING TWO NOTES BEFORE ASKING QUESTIONS • Unless otherwise stated it is fine to leave your answers as closed-form

test4a.pdf - PLEASE READ THE FOLLOWING TWO NOTES BEFORE...

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PLEASE READ THE FOLLOWING TWO NOTES BEFORE ASKING QUESTIONS: Unless otherwise stated, it is fine to leave your answers as closed-form expressions involving exponentials, factorials, and combinatorial symbols such as P ( n,k ), C ( n,k ), or ( n k ) . On multipart questions where you are asked how many objects there are satisfying certain restrictions, the restrictions in each part are independent of the restrictions in the other parts. So for example, the restriction in question 3(b) does not apply to question 3(c). 1. [6 points] The president of a college needs to choose a committee consisting of six faculty from the Computer Science and Engineering Departments. There are 18 faculty in the Computer Science Department and 23 faculty in the Engineering Department. (a) How many ways are there to select the committee? (b) How many ways are there to select the committee so that there are exactly three faculty from each department? (c) How many ways are there to select the committee so that there is at least one faculty member from each of the departments?
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  • Fall '07
  • Jarecki

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