High School Math Help: Combinations and Permutations
In high school, you'll learn lots of important statistics and probability concepts, including how to use permutations and combinations to calculate probabilities. Read on for a stepbystep explanation!
Permutations and Combinations
High school students learn to calculate the number of possible combinations or permutations in a given situation, and then find the probability that a particular one will occur. Here's a sample problem:
For an upcoming field trip, Amanda's teacher is dividing her 20student class into groups of four students. What is the probability that Amanda will be in a group with her three best friends, Sammy, Leslie and Jamie?
The probability that these four students will be in a group together is one out of the total number of combinations the teacher could choose. Keep reading to learn formulas for calculating combinations and permutations in different scenarios!
Permutation Formulas
When you calculate the number of ways you can arrange a set of things, each possible arrangement is called a permutation. For instance, each of the 5digit lottery numbers you can draw from the digits one through five is a permutation. A permutation without repetition means you can only use each digit once per permutation.
The formula for this is n!, where n is the number of things you're arranging and n! = (n) x (n  1) x (n  2) x … x (1). If n = 5, then n! = 5 x 4 x 3 x 2 x 1 = 120. This means that 120 different lottery numbers are possible.
You'll also need to calculate permutations without repetition when you're choosing a few things out of a larger group. For instance, to calculate how many 3digit lottery numbers you can draw from the numbers one through five, use the formula n!/(n  r)!, where n is the total number of possibilities (five) and r is the number of items in each permutation (three).
Sometimes, permutations are allowed to contain repeating digits. For instance, your locker number could be 11111 or 99888. This is called a permutation with repetition. The formula to calculate this is n^r, where n is the number of choices for each digit, and r is the number of digits in each permutation.
Combination Formulas
With permutations, we count the number of ways that things can be arranged. With combinations, we only count the number of possible groupings. Going back to the example with Amanda, there are lots of different ways we could arrange her and her friends if they were standing in a line. However, we can make just one combination with these four students, because we're only concerned with who's in the group, not the physical order in which they're arranged.
To calculate the number of 4student combinations we can make out of Amanda's entire 20student class, we need to use the formula for combinations without repetition: n!/r!(n  r)!. In this example, n = 20 and r = 4. There is no repetition because we can't have the same person in a group twice.
Sometimes, you can have repetition within combinations. For instance, if you're choosing a combination of three pizza toppings out of a list of ten, you could choose pepperoni, olives and mushrooms or just a triple order of pepperoni. To calculate the number of possible combinations with repetition, use this formula: (n + r  1)!/r!(n  1)!.
Other Articles You May Be Interested In

Imagine a math teaching tool so effective that it need only be employed twice per week for less than an hour to result in huge proficiency gains. Impossible, you say? Not so...and MIND Research Institute has the virtual penguin to prove it.

Should kindergartners put away the building blocks and open the math books? According to recent research, earlier is better when it comes to learning mathematical concepts. But that could put undue pressure on kids, parents and even teachers.
We Found 7 Tutors You Might Be Interested In
Huntington Learning
 What Huntington Learning offers:
 Online and incenter tutoring
 One on one tutoring
 Every Huntington tutor is certified and trained extensively on the most effective teaching methods
K12
 What K12 offers:
 Online tutoring
 Has a strong and effective partnership with public and private schools
 AdvancEDaccredited corporation meeting the highest standards of educational management
Kaplan Kids
 What Kaplan Kids offers:
 Online tutoring
 Customized learning plans
 RealTime Progress Reports track your child's progress
Kumon
 What Kumon offers:
 Incenter tutoring
 Individualized programs for your child
 Helps your child develop the skills and study habits needed to improve their academic performance
Sylvan Learning
 What Sylvan Learning offers:
 Online and incenter tutoring
 Sylvan tutors are certified teachers who provide personalized instruction
 Regular assessment and progress reports
Tutor Doctor
 What Tutor Doctor offers:
 InHome tutoring
 One on one attention by the tutor
 Develops personlized programs by working with your child's existing homework
TutorVista
 What TutorVista offers:
 Online tutoring
 Student works oneonone with a professional tutor
 Using the virtual whiteboard workspace to share problems, solutions and explanations