# Combinations Worksheets

What Are Statistical Combinations? When you are in the middle of statistical experiments, finding the total number of points in a sample can be hard or tedious. Thus, to make the counting task much easier, there are a few methods that can save us both time and effort. One of those methods is known as combinations. Combinations are a selection of the part of or all of a set of objects without considering the order in which these objects are selected. For instance, if we have three letters, X, Y and Z, then you can ask in how many ways you can select 2 letters from the set. To put it generally, n number of objects can be arranged in the form of n(n-1)(n-2)...(n – r + 1)/r! = n!/r!(n-r)! = nCr. Now, if we consider our example, there are three letters, X, Y, Z, then, n is 3, while r is 2 for this problem. The number of combinations is 3C2 = 3! / 2!(3 - 2)! = 3! /2!1! = (3)(2)(1)/(2)(1)(1) = 3.

• ### Basic Lesson

To find all of the different ways to arrange r items out of n items. Use the combination formula below. n stands for the total number of items; r stands for how many things you are choosing.

• ### Intermediate Lesson

Explains how to use the Combination formula. Practice problems are provided. There are 12 boys and 14 girls in class. Find the number of combinations of how a team of 3 students can be selected from the class to work together. The team consists of 3 students.

• ### Independent Practice 1

Contains 20 combinations problems. The answers can be found below.

• ### Independent Practice 2

Features another 20 Closure Property problems.

• ### Homework Worksheet

Find the combinations in selecting the following. Example problems are provided and explained.

• ### Topic Quiz

How many combinations of twelve letters are possible from the letters A to O? A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Which Mathematician?

This mathematician is best known for his work combining applications of algebra to geometry. He has a plane named after him, Who is he?