Pg. 606 Homework

• Pg. 631 #1 – 3, 5 – 10, 13 – 19 odd

• #11 35 #12 126• #13 70 #14 220• #15 1365 #16 1716 • #17 56x5y3 #18 56x3y5

• #19 240x4 #20 -2268x6

• #34 expand to prove

11.3 Counting, Permutations, and Combinations

Problem A:• How many two letter “words” can

be formed from the letters {a, b, c}?

Problem B:• A construction crew has three

members. A team of two must be chosen. In how many ways can the team be chosen from {a, b, c}?

• How are these two examples the same?

• How are these two examples different?

• Problem A is a _____________• Problem B is a _____________

11.3 Counting, Permutations, and Combinations

• A permutation of n objects taken r at a time, denoted P(n, r)is an arrangement of r of the n objects in a specific order.

• P(n, r) = n (∙ n – 1) (∙ n – 2) … ∙ ∙(n – (r – 1))

• P(5, 2)

• P(4, 2)

• P(3, 2)

• P(6, 4)

• P(100, 2)

11.3 Counting, Permutations, and Combinations

• A combination of n objects taken r at a time, denoted C(n, r)is a selection of r objects from among the n, with order disregarded.

• C(n, r) = P(n, r) r!

• C(5, 2)

• C(4, 2)

• C(3, 2)

• C(6, 4)

• C(100, 2)

11.3 Counting, Permutations, and Combinations

• When dealing with word problems, you must think:“Is there a specific order or is order disregarded?”

• This will tell you whether or not it is a permutation or combination.

• The Board of Directors of a company has 10 members. In how many ways can they choose a committee of three?

11.3 Counting, Permutations, and Combinations

• Nine horses are entered into the Kentucky Derby. Assuming no ties, how many different outcomes of 1st, 2nd, and 3rd are there?

• A student is require to work exactly five of the eight problems on an exam. In how many different ways can the problems be chosen?

11.3 Counting, Permutations, and Combinations

• How many different outcomes of “winner” and “runner-up” are possible if there are six contestants in a pie-eating contest?