Algebra IIAlgebra II10.1: Apply the Counting Principle 10.1: Apply the Counting Principle

and Permutationsand Permutations

HW: HW: p.686-688 (6, 10, 14, 16, 26,

28, 34, 62-68 all)

Quiz 10.1-10.3: Friday, 12/13

Fundamental Counting Fundamental Counting PrinciplePrinciple

If one event occurs If one event occurs mm ways and ways and another event occurs another event occurs nn ways, then ways, then both events occur ways.both events occur ways.

(Can be applied for more than two (Can be applied for more than two events.)events.)

Application of Fundamental Application of Fundamental Counting PrincipleCounting Principle

You have 3 shirts, 4 pairs of pants, You have 3 shirts, 4 pairs of pants, and 2 pairs of shoes. How many and 2 pairs of shoes. How many outfits of 1 shirt, 1 pair of pants, and outfits of 1 shirt, 1 pair of pants, and 1 pair of shoes can you create?1 pair of shoes can you create?

Application of Fundamental Application of Fundamental Counting PrincipleCounting Principle

How many different license plates are How many different license plates are possible if you have 1 letter followed by 2 possible if you have 1 letter followed by 2 digits followed by 3 letters if letters and digits followed by 3 letters if letters and digits can repeat? digits can repeat?

How many plates are possible if letters How many plates are possible if letters and digits cannot repeat?and digits cannot repeat?

FactorialFactorial What does 9! mean?What does 9! mean?

Expand and simplifyExpand and simplify1.) 2.)

3.) 4.)

PermutationsPermutations An ordering of n objects where An ordering of n objects where

order is important is a order is important is a permutation of the objects.permutation of the objects.

The number of permutations of n The number of permutations of n objects is n!.objects is n!.

Example:Example:– 10 people are in a race. How many 10 people are in a race. How many

different ways can the people different ways can the people finish in the race?finish in the race?

PermutationsPermutations The # of permutations = where The # of permutations = where

n = total # of objects, r = # you are n = total # of objects, r = # you are taking.taking.

Example: Example: – 10 people are in a race. 10 people are in a race. How many How many

different ways can 3 people win 1different ways can 3 people win 1stst, , 22ndnd, and 3, and 3rdrd place? place?

PermutationsPermutations You are burning a CD with 13 You are burning a CD with 13

songs. How many ways can the songs. How many ways can the songs be arranged on the CD?songs be arranged on the CD?

PermutationsPermutations Ms. Wynes’s 2Ms. Wynes’s 2ndnd period class is period class is

playing 7up with a total of 19 playing 7up with a total of 19 students in the class. How many students in the class. How many different ways can the people be different ways can the people be chosen if order is important?chosen if order is important?

Permutations with Permutations with RepetitionRepetition The number of permutations of The number of permutations of nn

objects where an object repeats objects where an object repeats ss # # of times.of times.

Find the number of distinguishable Find the number of distinguishable permutations of the letters in the permutations of the letters in the

word.word.1.) WYNES1.) WYNES

2.) TALLAHASSEE2.) TALLAHASSEE

3.) MATAWAN3.) MATAWAN

Find the number of distinguishable Find the number of distinguishable permutations of the letters in the permutations of the letters in the

word.word.4.) ABERDEEN4.) ABERDEEN

5.) CLASSROOM5.) CLASSROOM

6.) MATH6.) MATH