Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How...

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Transcript of Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How...

PermutationsCOUNTING!

What is a Permutation? Permutations essentially answer the question “How many ways?”

When we talk about permutations, the ORDER in which things happen matters

For example, Alice, Bob, and Charlie is different than Charlie, Bob, and Alice

ORDER MATTERS!

Page 3: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Permutations Permutations are different than Combinations in the sense that order does not matter when we are calculating combinations

In the case of a combination, Alice, Bob, and Charlie is the same as Charlie, Bob and Alice.

It is the same COMBINATION of names

Page 4: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Page 5: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Page 6: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example How many ways can I rearrange the five books?

Page 7: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Is there an easier way?

Page 8: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Page 9: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Page 10: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Try Another Example How many ways can you rearrange 8 different books?

Page 11: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Question What if we have 8 books but there are only three places on the shelf? How many ways can we rearrange the three books on the shelf?

Page 12: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Try It You have 10 books and want to arrange 4 on a shelf. How many ways can you do it?

Page 13: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Page 14: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Let’s Check with our Last Question

Page 15: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

How many ways can you arrange your 10 books on a four book shelf?

Page 16: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Correct Notation

Page 17: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example Evaluate:

₄P₂

₇P₃

₆P₅

Page 18: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example

Page 19: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example How many ways can you rearrange the letters in GUITAR?

Page 20: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example How many ways can you rearrange the letters in booger?

Page 21: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example Cont.

Page 22: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example How many ways can we rearrange the letters in Mississippi?

Page 23: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example 10 Students are running for student council. How many ways can they be selected as President, Secretary, and Treasurer?

Page 24: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example How many different six-digit numerals can be written using all of the following six digits: 4,4,5,5,5,7

Page 25: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example In how many different ways can Travis, Noah, Kyle, Heather, Michael, Jacob, and Cody stand in line?

Page 26: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Example Six coins are tossed at a time. How many outcomes show 4 heads and 2 tails?

Sect. 12-2 Permutations. Def: When a group of objects or people are arranged in a certain order, the arrangement is called a permutation.

Permutations, Combinations and the Binomial …faculty.washington.edu/moishe/hanoiex/counting/...Permutations, Combinations and the Binomial Theorem Permutation, revisited Deﬁnition

“Best” permutation for each model type determined by ranking RMSE, variance ratio, bias, and R 2 (Table 5). Arizona favored less complex variable permutations.

Permutations Combinations - Wikispaces6+-+Permutations... · Permutations Combinations Order ... Explain the difference between the permutation and combination formula and why. _____

Group Theory and the Rubik's CubeNote that a cycle of odd length is an even permutation. Likewise, a cycle of even length is an odd permutation. We will multiply permutations from

A permutation n distinct - Eastern Illinois University | …mathcs/mat2120/index/set04.pdfA permutation of n distinct objects is an arrangement or ordering of the n objects. The permutations

More Recursion: Permutations and Towers of Hanoi · Recursive Permutation Algorithm Recursive Permutation code in detail: 2 parameters to the function 1) The string we want to permute

SESSION 4 Permutations Combinations Polynomialsstudentsonline.btps.ca/documents/general/R3 Session 4 -- Perms... · A permutation is an arrangement of objects in a definite order.

Random permutation statistics - uni-stuttgart.depnp.mathematik.uni-stuttgart.de/iadm/Riedel/papers/RPS.pdfNumber of permutations that are mth roots of unity This generalizes the concept

Chapter 9jackmathsolutions.com/images/Chapter_9_Counting-Permuations... · 226 Chapter 9 9. Counting Permutations/Combinations Permutations A permutation of a number of objects is

5.Permutations and Combinations - Sakshi · 2014-10-30 · PERMUTATIONS AND COMBINATIONS Permutations are arrangements of things taken some or all at a time. In a permutation, order

Permutations, Combinations & Counting Principle Essential Questions: What’s the difference between a permutation & combination? When do we use the.

Permutation Pattern Matching for Separable Permutations.igm.univ-mlv.fr/AlgoB/slides/Neou_SPIRE_2016.pdf · Permutation Pattern Matching for Separable Permutations. Both Emerite Neou1,

3.4B-Permutations Permutation: ORDERED arrangement of objects. # of different permutations (ORDERS) of n distinct objects is n! n! = n(n-1)(n-2)(n-3)…3·2·1.

Permutations and Combinations. Objectives Calculate a permutation. Calculate a combination. Determine whether you should use a combination or permutation.

ariste Galois and Solvable Permutation Groupsjlipman/553/Cox-Galois.pdf · For Galois, permutations are bijections {1,...,m}−→{roots} ⇐call these arrangements while substitutions

Permutations, Combinations and the Binomial TheoremPermutations, Combinations and the Binomial Theorem November 24, 2010 Permutations, Combinations and the Binomial Theorem. Permutation,

1 Pruned Bit-Reversal Permutations: Mathematical ... · Bit-reversal permutations, pruned interleavers, turbo interleavers, permutation polynomials, permutation statistics. I. INTRODUCTION

Permutations and Combinations. Perms A permutation is an ordered arrangement of objects An r-permutation is an ordered arrangement of size r The number.

Algorithms for permutations and combinations, with and ... · Algorithms for permutations and combinations, with and without repetitions ... A permutation of size r of a range of

Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How...

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