3.4 counting principles i.the fundamental counting principle: if one event can occur m ways and a...

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3.4 Counting Principles I. The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the 2 events can occur in sequence is m x n. Page 150-151 Examples 1 & 2

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Page 1: 3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the

3.4 Counting Principles

I. The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the 2 events can occur in sequence is m x n.

Page 150-151 Examples 1 & 2

Page 2: 3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the

II. Permutations

• An ordered arrangement of objects• The number of different permutations of n

distinct objects is n!• Factorial: n! = n(n-1)(n-2)…• P152 Example 3

•nPr = n! The number of permutations of n

(n-r)! distinct objects taken r at a time

• P152-153 Examples 4 & 5

Page 3: 3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the

• Distinguishable Permutations:

• P154 Example 6 and TIY6

Page 4: 3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the

III. Combinations

• A selection of r objects from a group of n objects without regard to order

• nCr = n!

(n-r)!r!

• P155 Example 7 and TIY#7

Page 5: 3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the

IV. Applications of Counting Principles1. A word consists of 1 M, 4 Is, 4 Ss, and 2

Ps. If the letters are randomly arranged in order, what is the probability the arrangement spells the word Mississippi?

Page 6: 3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the

2. A word consists of 1 L, 2 Es, 2 Ts, and 1 R. If the letters are randomly arranged in order, what is the probability the arrangement spells the word Letter?

Page 7: 3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the

3. Find the probability of being dealt five diamonds from a standard deck of playing cards. (In poker, this is a diamond flush.)

Page 8: 3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the

4. A jury consists of 5 men and 7 women. Three are selected at random for an interview. Find the probability that all three are men.

• P158 #24-38even

#47 Give three common ways that matter is measured. Give examples of each Counting: Example, counting sheep Volume: Example: estimating the # of jelly

Counting Techniques Sue Gordon - University of Sydney€¦ · The ﬁrst box can be ﬁlled in 6 ways, the second in 5 ways and the third in 4 ways, ie the number of permutations

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Counting Scalecounting applications. FC-i counting scale: 1/1,000,000 FC-Si counting scale: Up to 1/10,000,000 There are the following ways to enter a unit weight (of the sample piece)

How Many Is Too Many - · Web viewEncourage your child to chant the counting ... Counting in . Different Ways ... mittens, eyes in your family); or fives (fingers, toes); or tens (fingers,

Running head: COUNTING TWO WAYS Counting Two Ways: …sigmaa.maa.org/rume/crume2010/Archive/Engelke.pdfCounting Two Ways: The Art of Combinatorial Proof When studying the thought processes

Counting Principles The Fundamental Counting Principle: If one event can occur m ways and another can occur n ways, then the number of ways the events

PROBABILTY P= number of ways that a given outcome can occur total number of possible outcomes P= number of ways that a given outcome can occur total

Counting, Permutations, & Combinations. A counting problem asks “how many ways” some event can occur. Ex. 1: How many three-letter codes are there using

Chance of winning Unit 6 Probability. Multiplication Property of Counting If one event can occur in m ways and another event can occur in n ways, then

St. Cyril Catholic School News · pumpkins and counting the seeds. The students are counting to make to 30, finding different ways of making 10, recognizing and printing numbers

Fundamental Counting Principle - Weebly€¦ · Fundamental Counting Principle - Uses multiplication of the number of ways each event in an experiment can occur to ﬁnd the number

The Mole. Matter can be measured in 3 ways: Counting particles Mass Volume

Loudoun County Public Schools / Overview...Fundamental Counting Principle, Combinatorics Fundamental Counting Principle. If one event can occur in m ways and a second event can occur

Chapter 6: Chemical Reactions Occur in Predictable Ways Science 10 Chemistry Unit p.254-283

Counting and Probability Counting -

Probability Chapter 3. Methods of Counting The type of counting important for probability theory involves choosing the number of ways we can arrange

Counting Trees - Brown University · 2020-04-29 · Counting Trees Attempt 2: Building up Ways to add a vertex So, let’s be careful to only generate trees. Here’s the thought

More Counting. Probability.Combinatorial Proofs: Identity from counting same in two ways. Pascal’s Triangle Example: n+1 k = n k 1 + n k. RHS: Number of subsets of n+1 items size

Counting Techniques 0.4. Fundamental Counting Principal TWO EVENTS: If one event can occur in m ways and another event can occur in n ways, then the number

Fundamental Counting Principle, Permutations and …juliehuber.weebly.com/uploads/5/4/0/3/54030645/hpcrpc_fundamental... · Fundamental Counting Principle The number of ways in which

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Basic Concepts of Probability and Counting Section 3lam/su131040/Section.3.1.pdf · This is the fundamental counting principle: The number of ways two events can occur in sequence

Counting output in ways that matter: lessons from Britains Railways …or… Dr Tim Leunig & Professor Nick Crafts

How Many Ways Can We Tile a Rectangular Chessboard …math.cmu.edu/~bwsulliv/domino-tilings.pdf · How Many Ways Can We Tile a Rectangular Chessboard With Dominos? Counting Tilings

Counting ScaleThe scales have the high internal resolution for a wider range of counting applications. HC-3Ki / 6Ki / 30Ki: 1/600,000 HC-15Ki: 1/750,000 There are the following ways