Algebra 2 Equations and inequalities Overview Solve equations and simplify expressions Line plots and stem-and-leaf plots Absolute value Solve inequalities. Algebra 2 How to graph functions and linear equations Overview Functions and linear equations Graph functions and relations Graph inequalities. Algebra 2 How to solve system of linear equations Overview Solving systems of equations in two variables Solving systems of equations in three variables.
Algebra 2 Matrices Overview Basic information about matrices How to operate with matrices Determinants Using matrices when solving system of equations.
Algebra 2 Polynomials and radical expressions Overview Simplify expressions Polynomials Factoring polynomials Solving radical equations Complex numbers.
Algebra 2 Quadratic functions and inequalities Overview How to graph quadratic functions How to solve quadratic equations The Quadratic formula Standard deviation and normal distribution. Algebra 2 Conic Sections Overview Distance between two points and the midpoint Equations of conic sections.
For this calculator, the order of the items chosen in the subset does not matter. Also referred to as r-combination or "n choose r" or the binomial coefficient. In some resources the notation uses k instead of r so you may see these referred to as k-combination or "n choose k. You have won first place in a contest and are allowed to choose 2 prizes from a table that has 6 prizes numbered 1 through 6. How many different combinations of 2 prizes could you possibly choose?
In this example, we are taking a subset of 2 prizes r from a larger set of 6 prizes n. A teacher is going to choose 3 students from her class to compete in the spelling bee. In other words it is now like the pool balls question, but with slightly changed numbers. And we can write it like this:.
But knowing how these formulas work is only half the battle. Figuring out how to interpret a real world situation can be quite hard. To help you to remember, think " P ermutation P osition". Example: what order could 16 pool balls be in? After choosing, say, number "14" we can't choose it again. Examples: 4! It may seem funny that multiplying no numbers together gets us 1, but it helps simplify a lot of equations.
Example Our "order of 3 out of 16 pool balls example" is: 16! Example: How many ways can first and second place be awarded to 10 people? For example, let us say balls 1, 2 and 3 are chosen. These are the possibilites: Order does matter Order doesn't matter 1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1 1 2 3. A factorial represents the product of all numbers from 1 up to and including the specified number.
Define the variables. To best understand the concept, let's work through an example. Let's look at the number of ways 13 playing cards can be selected from a deck of The first card selected can be any one of the 52 cards. The second number selected is taken from 51 cards and so on.
Review the formula for combinations. The formula for combinations is generally n! Substitute the variables into the formula. To know how many combinations of 13 can be selected from a deck of 52 cards, the equation is 52!
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