FUNDAMENTALS OF ALLGEBRA 2A CHAPTER 11 POWERPOINT

PRESENTATION

PERMUTATIONS, COMBINATIONS, AND PROBABILITY

LEARNING TARGETS

• AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO:

• USE THE FUNDAMENTAL PRINCIPLE OF COUNTING

• DETERMINE THE NUMBER OF PERMUTATIONS AND COMBINATIONS

• FIND THE PROBABILITY OF EVENTS• USE BINOMIAL THEOREM• IDENTIFY SEQUENCES

CHAPTER VOCABULARY

• TREE DIAGRAM: A CHART WITH BRANCHES THAT SHOW RELATIONSHIPS

• FUNDEMENTAL PRINCIPLE OF COUNTING: COUNTING EVENTS: if one task can be completed (p) different ways and a second task can be completed (q) different ways, then the first task followed by the second can be completed in (pq) different ways.

• MULTIPLICATION PRINCIPLE: THE FORMULA TOTAL NUMBER OF SELECTIONS IN SUCCESSION

TREE DIAGRAM

Fundamental Principle of Counting

MULTIPLICATION PRINCIPLE

PERMUTATIONS

• PERMUATIONS: THE ARRANGEMENT OF OBJECTS IN A SPECIFIC ORDER.

PERMUTATION/COMBINATION FORMULA

Combinations

• Combinations: An arrangement of a group of objects in which order is not important.

FORMULA FOR COMBINATIONS

Sample With Replacement

• Suppose you have a bag of marbles: All together there are 10 marbles: 3 are black, 4 are red, 2 are yellow, and 1 is green.

• If you take a marble out and replace it, you will still have:

• 3/10 it is black, 2/5 it is red, 1/5 it is yellow, and 1/10 it is green. The odds do not change when you replace the item you pulled.

BASIC PROBABILITY

• EVENT: AN INDIVIDUAL OUTCOME OF ANY SPECIFIED COMBINATIONS OF OUTCOMES.

• PROBABILITY FRACTION: THE NUMBER OF FAVORABLE OUTCOMES DIVIDED BY THE TOTAL NUMBER OF POSSIBLE OUTCOMES.

• COMPELMENTARY EVENT: AN OUTCOME THAT CAN BE FAVORABLE OR UNFAVORABLE ACCOMPANYING A PARTICULAR EVENT.

SPINNERS, NUMBER CUBES, MARBLES IN BAGS, ETC.

• PROBABILTY EVENTS CAN BE FOUND ON: SPINNERS, MARBLES IN BAGS, NUMBER CUBES(FORMERLY KNOWS AS DICE), LETTERS IN THE ALPHABET, ETC.

BINOMIAL THEOREM

• A WAY TO WRITE COMBINATIONS:

PASCAL’S TRIANGLE

• IF YOU WRITE COEFFICIENTS SEPARATELY, YOU WILL GET A BEAUTIFUL PATTERN KNOWN AS PASCAL’S TRIANGLE:

ARITHMETIC SEQUENCES: VOCABULARY

• SEQUENCE: AN ORDERED LIST OF NUMBERS.• ARITHMETIC SEQUENCE: A SEQUENCE IN

WHICH SUCCESSIVE TERMS DIFFER BY THE SAME NUMBER, (d), CALLED THE COMMON DIFFERENCE.

• COMMON DIFFERENCE: THE CONSTANT, (d), ADDED TO A TERM IN AN ARITHMETIC SEQUENCE TO GET THE NEXT TERM.

MORE VOCABULARY

• SERIES: THE INDICATED SUM OF THE TERMS OF A SEQUENCE.

• DERIVATION: A SEQUENCE OF STATEMENTS THAT SHOWS A RESULT IS A CONSEQUENCE OF ACCEPTED STATEMEMENTS.

• GEOMETRIC SEQUENCE: A SEQUENCE IN WHICH SUCCESSIVE TERMS DIFFER BY THE SAME RATIO (r), CALLED THE COMMON RATIO.

GEOMETRIC MEAN

• GEOMETRIC MEAN: THE SQUARE ROOT OF THE PRODUCT OF TWO NUMBERS. THE GEOMETRIC MEAN BETWEEN A AND B, IS THE SQUARE ROOT OF AB.

• YOU CAN ALWAYS CREATE A GEOMETRIC SEQUENCE OF THREE TERMS BY FINDING THE GEOMETRIC MEAN BETWEEN TWO NUMBERS.

SIGMA NOTATION

• SIGMA IS A LETTER IN THE GREEK ALPHABET AND IT IS USED AS A SYMBOL FOR SUM.

• A SUBSCRIPT IS USED TO SHOW THE FIRST TERM.

• A SUPERSCRIPT IS USED TO SHOW THE LAST TERM.

Sigma Notation

TERMS

• CONVERGENT SERIES: AN INFINITE SERIES WHOSE PARTIAL SUMS APPROACH A FIXED NUMBER AS (n) INCREASES.

• DIVERGENT SERIES: AN INFINITE SERIES WHOSE PARTIAL SUMS DO NOT APPROACH A FIXED NUMBER AS (n) INCREASES.

I LOVE MATH!Permutations!!!!