6.7 Permutations and Combinations

Jan 22, 2014

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Permutations and Combinations. Simplify each expression.1.10

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6.7 Permutations and Combinations

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Permutations and Combinations

Permutations and Combinations. Making your own starting lineup!. Why do we want to study permutation and combination?. Very often we will find situations where one thing can be done in different ways. In order to find the best way, we need to know how many possible ways are there in total.

830 views • 9 slides

Permutations and Combinations

CSE 2813 Discrete Structures. Permutations. Permutation: A set of distinct objects in an ordered arrangement of these objects.r-permutation: An ordered arrangement of r elements of a set.Example: Consider the set S = {1,2,3}.What are the 3-permutations of S ?What are the 2-permutations of S ?.

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Permutations and Combinations

Permutations and Combinations. CS/APMA 202 Rosen section 4.3 Aaron Bloomfield. Permutations vs. Combinations. Both are ways to count the possibilities The difference between them is whether order matters or not Consider a poker hand: A ♦, 5♥, 7♣, 10♠, K♠ Is that the same hand as:

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6.7 Permutations and Combinations

6.7 Permutations and Combinations. Def: A permutation is an arrangement of items in a particular order. Ex. How many ways can 10 books be line up on a shelf? Answer: 10*9*8*7*6*5*4*3*2*1 = 3,628,800 Def: n factorial For any positive integer n, n!= n*(n-1)*(n-2) … 3*2*1 For n=0, n!=1.

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Notes 6.7 Permutations and Combinations

Notes 6.7 Permutations and Combinations. Permutation – an arrangement of items in a particular order Can use the counting principle or factorials to solve. Factorial: n! = n(n – 1)… 3! = 3*2*1 = 6 4! = 4*3*2*1 = 24 0! = 1. EX 1. In how many ways can 6 people line up?. EX 2.

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Permutations and Combinations

Permutations and Combinations. In this section, techniques will be introduced for counting the unordered selections of distinct objects and the ordered arrangements of objects of a finite set. 6.2.1 Arrangements.

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Permutations and Combinations

Permutations and Combinations. Objectives:. apply fundamental counting principle compute permutations compute combinations distinguish permutations vs combinations find probabilities using permutations and combinations. Fundamental Counting Principle.

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Permutations and Combinations

Permutations and Combinations . Solve Counting Problems Using Multiplication Principle Solve Counting Problems Using Permutations Solve Counting Problems Using Combinations Solve Counting Problems Using Permutations involving non distinct objects. Multiplication Principle of Counting.

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Permutations and Combinations

In this lesson we single out two important special cases of the Fundamental Counting Principle—permutations and combinations. Goal: Identity when to use permutations and combinations. . Permutations and Combinations. Permutation .

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Permutations and Combinations

MDM 4U: Mathematics of Data Management Unit: Counting and Probability By: Mr. Allison and Mr. Panchbhaya. Permutations and Combinations. Specific Expectations. Strand 2.1

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PERMUTATIONS AND COMBINATIONS

PERMUTATIONS AND COMBINATIONS. PERMUTATIONS AND COMBINATIONS ARE METHODS TO SOLVE CERTAIN TYPES OF WORD PROBLEMS. BOTH PERMUTATIONS AND COMBINATIONS USE A COUNTING METHOD CALLED FACTORIAL . A FACTORIAL is a counting method that uses consecutive whole numbers as factors.

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Permutations and Combinations

Permutations and Combinations. Lesson 8 HAND OUT REFERENCE SHEET AND GO OVER IT. Permutations vs. Combinations. Both are ways to count the possibilities The difference between them is whether order matters or not Consider a poker hand: A ♦, 5♥, 7♣, 10♠, K♠ Is that the same hand as:

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Permutations and Combinations

Permutations and Combinations. PRE-ALGEBRA LESSON 12-6. Bianca’s family needs to choose exterior paint for their new house. The wall colors are white, green, and beige. The trim colors are white, green, blue, and cocoa. How many combinations of wall color and trim are possible?. 12. 12-6.

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6.7 Permutations & Combinations

6.7 Permutations & Combinations. Permutations / Combinations. I. Permutations A) Factorials B) Permutations n P r n! (n-r)! II. Combinations n C r n! r! (n-r)!. Factorials !. 5! 5x4x3x2x1 = 120 How many ways can 10 people line up in a straight line?

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Permutations and Combinations

Permutations and Combinations. No HW. When you count the total number of possibilities , you have to decide whether order matter. Problems. We have 3 cards A B C. How many ways are there of arranging them?. ABC ACB BAC BCA CBA CAB – 6 A quicker way would be. Read through.

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Permutations and Combinations

Permutations and Combinations. Pg 1.2 and WS #1: How many different ways can you line up 5 skittles, each a different color ? Pg 1.3 and WS#2: How many different ways can you line up just 3 of the 5 skittles ?

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Permutations and Combinations

Permutations and Combinations. Perms. A permutation is an ordered arrangement of objects An r-permutation is an ordered arrangement of size r The number of r-permutations of a set of size n is P(n,r) = n(n-1)(n-2) … (n-r) n ways to choose 1st object

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Permutations and Combinations

Permutations and Combinations. ictlab.tyict.vtc.edu.hk/~steveng/ITD1111/Lecture/07.%20CountPro2. ppt. 6.2.1 Arrangements. The number of ways of arranging n unlike objects in a line is n ! . Note: n ! = n (n-1) (n-2) ···3 x 2 x 1. Example.

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PERMUTATIONS and COMBINATIONS

CHAPTER 7. PERMUTATIONS and COMBINATIONS. 7.1 – Permutations. 7.2 – Combinatons. 1. 9.1 – Permutations. OBJECTIVES. a) Understand the techniques of counting. b) Understand permutations of a set of objects with some conditions. 2. Permutation of a set of objects. 3. 4.

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Permutations and Combinations

Permutations and Combinations. Rosen 4.3. Permutations. A permutation of a set of distinct objects is an ordered arrangement these objects. An ordered arrangement of r elements of a set is called an r-permutation. The number of r-permutations of a set with n elements is denoted by P(n,r).

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Permutations and Combinations

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6.7 Permutations and Combinations

6.7 Permutations and Combinations

Presentation Transcript

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

6.7 Permutations and Combinations

Notes 6.7 Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

PERMUTATIONS AND COMBINATIONS

Permutations and Combinations

Permutations and Combinations

6.7 Permutations &amp; Combinations

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

PERMUTATIONS and COMBINATIONS

Permutations and Combinations

Permutations and Combinations

6.7 Permutations & Combinations