5. Of a company's personnel, 7 works in design, 14 in manufacturing, 4 in testing, 5 in sales, 2 in accounting, and 3 in marketing. A committee of 6 people is to be formed to meet with upper management. (a) How many different committees can be formed? (b) In how many ways can the committee be formed if there is to be one member from each department? (c) In how many ways can the committee be formed if there must be exactly two members from manufacturing? (d) In how many ways can the committee be formed if the accounting department is not to be represented and marketing is to have exactly one representative?

Question
5. Of a company's personnel, 7 works in design, 14 in manufacturing, 4 in testing, 5 in
sales, 2 in accounting, and 3 in marketing. A committee of 6 people is to be formed to
meet with upper management.
(a) How many different committees can be formed?
(b) In how many ways can the committee be formed if there is to be one member from
each department?
(c) In how many ways can the committee be formed if there must be exactly two
members from manufacturing?
(d) In how many ways can the committee be formed if the accounting department is not
to be represented and marketing is to have exactly one representative?

Image Transcription

5. Of a company's personnel, 7 works in design, 14 in manufacturing, 4 in testing, 5 in sales, 2 in accounting, and 3 in marketing. A committee of 6 people is to be formed to meet with upper management. (a) How many different committees can be formed? (b) In how many ways can the committee be formed if there is to be one member from each department? (c) In how many ways can the committee be formed if there must be exactly two members from manufacturing? (d) In how many ways can the committee be formed if the accounting department is not to be represented and marketing is to have exactly one representative?

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