Of a company\'s personel, 7 work in design, 14 in manufacturing, 4 in testing, 5

Question

Of a company's personel, 7 work 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 ways can the committee be formed if there must be exactly 2 members form the manufacturing department?

b.) Lucy works in the design department and her husband works in marketing. How many ways can the committee be formed if they both cannot be on the committee?

c.) How many ways can the committee be formed if there must be at least 2 members from the manufacturing department?

Explanation / Answer

14 C 2 * 21 C 4 = 91 * 5985 = 544635 ways 33C6 = 1107568 14 C2 * 21 C 4 + 14 C3 * 21 C 3 + 14 C 4 * 21 C 2 + 14 C 5 * 21 C 1 + 14 C 6 * 21 C 0 = 544635 + 484120 + 210210 + 42042 + 3003 = 1284010 ways

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