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 Pre-algebra Arithmetics Integers Divisibility Decimals Fractions Exponents Percentages Proportional reasoning Radical expressions Graphs Algebra Monomials Polynomials Factoring Linear Equations Graphs of linear equations Rectangular Coordinate System Midpoint Formula Definition of Slope Positive and negative slope Determine the slope of a line Equations of lines Equation of lines (from graph) Applications of linear equations Inequalities Quadratic equations Graphs of quadratic equations Absolute Value Radical expressions Exponential equations Logarithmic equations System of equations Graphs and functions Plotting points and naming quadrants Interpreting Graphs Relations and Functions Function Notation Writing a Linear Equation from a Table Writing a Linear Equation to describe a Graph Direct Variation Indirect Variation Domain and range Sequences and series Matrices Inverse of a matrix Determinants Inner product Geometry Triangles Polygons 2-D Shapes 3-D Shapes Areas Volume Pythagorean Theorem Angles Building Blocks Geometry Transformations Parallel, coincident and intersepting lines Distances in the plane Lines in space Plane in space Angles in the space Distances in the space Similarity Precalculus Sequences and series Graphs Graphs Definition of slope Positive or negative slope Determine the slope of a line Equation of a line (slope-intercept form) Equation of a line (point slope form) Equation of a line from graph Domain and range Quadratic function Limits (approaches a constant) Limits (approaches infinity) Asymptotes Continuity and discontinuities Parallel, coincident and intersepting lines Introduction to Functions Limits Continuity Asymptotes Trigonometry Trigonometric ratios The reciprocal trigonometric ratios Trigonometric ratios of related angles Trigonometric identities Solving right angles Law of sines Law of cosines Domain of trigonometric functions Statistics Mean Median Mode Quartiles Deciles Percentiles Mean deviation Variance Standard Deviation Coefficient of variation Skewness kurtosis Frequency distribution Graphing statistics & Data Factorial Variations without repetition Variations with repetition Permutations without repetition Permutation with repetition Circular permutation Binomial coefficient Combinations without repetition Combinations with repetition

 Permutations without repetition A permutation is an arrangement, or listing, of objects in which the order is important. How many different ways are there to arrange your first three classes if they are math, science, and language arts? The arrangement of science, math, language arts is a permutation of math, science, language arts because the order of the classes is different. You can use the Fundamental Counting Principle to find the number of permutations. There are 6 possible arrangements, or permutations, of the 3 classes. The number of permutations of n elements is: Pn=n! (n factorial), where n is the number of elements of the set. In how many ways may 3 books be placed next to each other on a shelf? Since there are 3 books, the first place may be filled in 3 ways. There are then 2 books left, so that the second place many be filled in 2 ways. There is only 1 book left to fill the last place. Since the arrangement of books on the shelf is important, it is a permutations problem. p3=3!=3·2·1=6 Thus the books can be arranged in 6 ways. In general, when we are given a problem involving permutations, where we are choosing r members from a set with n members and the order is important, the number of permutations is given by the expression nPr=n · (n - 1) · (n - 2) · … · (n - r + 2) · (n - r + 1). The first factor indicates we can choose the first member in n ways, the second factor indicates we can choose the second member in n - 1 ways once the first member has been chosen, and so on. A license plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once? For the first letter, there are 5 possible choices. After that letter is chosen, there are 4 possible choices. Finally, there are 3 possible choices. 5P3=5 × 4 × 3 = 60 PERMUTATION FORMULA In general nPr means that the number of permutations of n things taken r at a time. We can either use reasoning to solve these types of permutation problems or we can use the permutation formula. The formula for permutation is:    $_nP_r=\frac{n!}{(n-r)!}$ A license plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once? The problem involves 5 things (A, B, C, D, E) taken 3 at a time. $_5P_3=\frac{5!}{(5-3)!}=\frac{5!}{2!}=\frac{5\cdot4\cdot3\cdot2!}{2!}=60$ There are 60 different permutations for the license plate. Enter the number of elements of the set A and the computer will calculate you how many permutations without repetition of the elements are there? Enter the number n = Pn =