5. Of a company's personnel, 7 works in design, 14 in manufacturing, 4 in testing, 5 insales, 2 in accounting, and 3 in marketing. A committee of 6 people is to be formed tomeet 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 fromeach department?(c) In how many ways can the committee be formed if there must be exactly twomembers from manufacturing?(d) In how many ways can the committee be formed if the accounting department is notto be represented and marketing is to have exactly one representative?

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Asked Nov 2, 2019
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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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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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Expert Answer

Step 1

(a) Obtain the number of different committees that can be formed as follows.

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Total number of members, n 35 Number of members in the committee, r 6 Number of different committees that can be formed =C(35,6) 35! 61(35-6) 35! 6! x 29! 1,623,160

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Step 2

(b) Obtain the number of different committees that can be formed if there is to be one member from each department as follows.

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(7,1)(14,1 (4,1)(5,1)(2,1)(3,1) =7 x 14x 4 x 5x 2 x 3 11,760

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Step 3

(c) Obtain the number of different committees that can be formed if there must...

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(14,2)(35-14,4) (14,2) ( 21,4) 14! 21! 2!(14-2) 4!(21-4)! =91x 5985 544,635

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