Pg. 606 Homework Pg. 631#1 – 3, 5 – 10, 13 – 19 odd #1135#12126 #1370#14220 #151365#161716 #1756x 5 y 3 #1856x 3 y 5 #19240x 4 #20-2268x 6 #34expand to.

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Pg. 606 Homework Pg. 631#1 – 3, 5 – 10, 13 – 19 odd #1135#12126 #1370#14220 #151365# #1756x 5 y 3 #1856x 3 y 5 #19240x 4 # x 6 #34expand 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 1 st, 2 nd, and 3 rd 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?