Advanced PrecalculusAdvanced Precalculus Notes 12.2 Permutations and Combinations

Tree diagram: A method of visualizing and listing an

experiment’s sample space.

Permutation: An ordered arrangement of r

objects chosen from n objects.

Combination: An arrangement, without

regard to order, of r objects selected from n distinct

objects without repetition.

),( rnP

Prn

),( rnC

Crn

A box has two red, two green and two white balls in it. If you draw two balls, one at a time, how many different outcomes can you get?

Multiplication Principle of Counting: If a task consists of a sequence of choices in which

there are p selections for the first choice, q selections for the second choice, r selections for the third choice and so on, then the task of making these selections can be done in ways. A fixed-priced dinner includes:Appetizer: Soup or saladEntrée: chicken, beef, fish, porkDessert: pie, cake, ice cream How many three course dinners can be ordered?

rqp

A 1958 Colorado license plate contained 2 letters and 3 numbers. How many license plates were created?

How many had no repetition of letters or numbers?How many different arrangements of the letters abcd are possible? How many distinguishable arrangements of the letters in the word banana are possible? In how many ways can 5 people be lined up?

Evaluate: a)P(7, 3) b) P(6, 1) c) (52, 5)

Isabelle, Eva and Amanda have different birthdays. If we listed all the possible ways this could occur, how many would there be? (based on 365 days in a year) List all the combinations of the 4 objects a, b, c, d taken 2 at a time. What is C(4, 2)?

Find the value of: a)C(3, 1) b) C(6, 3)

c) C(n, n) d) C(n, 0)

How many different committees of 3 people can be formed from a pool of 7 people? In how many ways can a committee consisting of 2 faculty members and 3 students be formed if 6 faculty members and 10 students are eligible to serve on the committee?

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