How many combinations probability

Table 1. Six Possible Orders. Number First Second Third 1 red yellow green 2 red green yellow 3 yellow red green 4 yellow green red 5 green red yellow 6 green yellow red. Table 2. Twelve Possible Orders. Number First Second 1 red yellow 2 red green 3 red brown 4 yellow red 5 yellow green 6 yellow brown 7 green red 8 green yellow 9 green brown 10 brown red 11 brown yellow 12 brown green.

Table 3. Six Combinations. Number First Second 1 red yellow 2 red green 3 red brown x yellow red 4 yellow green 5 yellow brown x green red x green yellow 6 green brown x brown red x brown yellow x brown green.

Permutations and Combinations Author s David M. Lane Prerequisites none Learning Objectives Calculate the probability of two independent events occurring Define permutations and combinations List all permutations and combinations Apply formulas for permutations and combinations This section covers basic formulas for determining the number of various possible types of outcomes.

Possible Orders Suppose you had a plate with three pieces of candy on it: one green, one yellow, and one red. We can also use Pascal's Triangle to find the values. Go down to row "n" the top row is 0 , and then along "r" places and the value there is our answer.

Here is an extract showing row Let us say there are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. Now, I can't describe directly to you how to calculate this, but I can show you a special technique that lets you work it out.

Think about the ice cream being in boxes, we could say "move past the first box, then take 3 scoops, then move along 3 more boxes to the end" and we will have 3 scoops of chocolate!

So it is like we are ordering a robot to get our ice cream, but it doesn't change anything, we still get what we want. We can write this down as arrow means move , circle means scoop. So instead of worrying about different flavors, we have a simpler question: "how many different ways can we arrange arrows and circles? Notice that there are always 3 circles 3 scoops of ice cream and 4 arrows we need to move 4 times to go from the 1st to 5th container.

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. Pre-Algebra Discover fractions and factors Overview Monomials and adding or subtracting polynomials Powers and exponents Multiplying polynomials and binomials Factorization and prime numbers Finding the greatest common factor Finding the least common multiple.

Pre-Algebra More about the four rules of arithmetic Overview Integers and rational numbers Learn how to estimate calculations Calculating with decimals and fractions Geometric sequences of numbers Scientific notation. Pre-Algebra More about equation and inequalities Overview Fundamentals in solving Equations in one or more steps Calculating the circumference of a circle.

Pre-Algebra Graphing and functions Overview Linear equations in the coordinate plane The slope of a linear function Graphing linear inequalities Solve systems of equations by graphing.

Pre-Algebra Introducing geometry Overview Geometry — fundamental statements Circle graphs Angles and parallel lines Triangles Quadrilaterals, polygons and transformations.

Compute the probability of randomly drawing five cards from a deck of cards and getting three Aces and two Kings. Suppose you have a room full of 30 people. What is the probability that there is at least one shared birthday?

Take a guess at the answer to the above problem. Suppose three people are in a room. What is the probability that there is at least one shared birthday among these three people? There are a lot of ways there could be at least one shared birthday. Fortunately there is an easier way. In other words, since this is a complementary event,. We will start, then, by computing the probability that there is no shared birthday.

Your birthday can be anything without conflict, so there are choices out of for your birthday. What is the probability that the second person does not share your birthday? Now we move to the third person.