Activity 4

Of a company's personnel, 7 people 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.

1. How many committees are possible?
• C(35,6)
• 35! / [29!*6!]
• 1,623,160
2. How many committees with 1 member from each department are possible?
• C(7,1) * C(14,1) * C(4,1) * C(5,1) * C(2,1) * C(3,1)
• 7 *14 * 4 * 5 * 2 * 3
• 11,760
3. How many committees with no members of manufacturing are possible?
• C(21,6)
• 21! / [15!*6!]
• 54,264
4. How many committees with exactly 2 members from manufacturing are possible?
• C(14,2) * C(21,4)
• 14!/[12!*2!] * 21! / [17!*4!]
• 544,635
5. How many committees with no representative from accounting and exactly 1 member from marketing are possible?
   • C(3,1) * C(30,5)
   • 3 * 30! / [25!*5!]
   • 427,518