Use either the Permutation or Combination Formula to determine the following ans

Question

Use either the Permutation or Combination Formula to determine the following answers.

a) There are 12 member in the local garden club. In how many ways can a president and secretary be chosen? (Assume that no member can hold positions at the same time.)

b)There are 8 people hosting a party. Three people must stay after the party for cleanup duty. In how many ways can the clean-up crew be chosen?

c) There are 8 people hosting a party. One person must set up the catering, another must bring flowers, and a third must bring the drinks. In how many ways can these tasks be assigned?

Explanation / Answer

a) Out of 12 member in the local garden club president and secretary needs to be choosed but no member can hold the positions. Therefore we can do 12 C 2 = 12 ! / (2! * (12 - 2)! ) = 12! / (2! * 10!) = 66ways

Thus there are 66 ways in which president and secretary can be choosed.

b) 8 people hosting a party . Three people must stay after the party for cleanup duty .

Therefore we can do 8C 3 = 8! / (3! * ( 8-3)! ) = 8! / (3! * 5!) = 56ways

Thus there are 56 ways in which we can choose three people which would stay after 8 people hosted party.

c) 8 people hosting party . One person set up the catering , 2nd for flowers , 3rd for drinks .

8c1 + 7c1 + 6c1 = 8! / (1! * (8-1)! ) + 7! / (1! * (7-1)! ) + 6! / (1! * (6-1)! ) = 8! / (1! * 7! ) + 7! / (1! * 6!) + 6! / (1! * 5!)

= 21 ways

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