Post on 03-Jan-2016
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?