Home > Math Worksheets > Statistics > Combination Probability

A combination is comprised of each of the different groups or selections which can be formed by taking some or all of a number of objects. In many situations, many different combinations are possible that will satisfy the situation. We use combination formula to find probability after selecting more than one items. Combination is the ways of r items from a set of n and you will denote combination by nCr. nCr = n!/r! (n-r)!, n! = 1 × 2x ... x n, 0! = 1, 1! = 1. Problems based in combination probability - Example # 1 - We have 9 white and 6 black balls in a bag and here, you will find the probability of combination. Choices: 1) 2 white balls 2) 3 white balls. Solution: Combination formula is nCr = n!/r!(n-r)! Probability of event A is: P (A) = Number of favorable outcomes/ total number of outcomes. 1) Find the probability of selected 2 white balls. You will get the favorable cases after selecting 2 balls from 9 white balls. You will do it by 9 C2 ways. There are 15 balls by adding 9 and 6. You will get the number of outcomes by choosing 2 balls from 15 balls and you do this by 15 C2 ways. The required probability will be 9 C3/15 C3. 2) Find the probability of choosing 3 white balls. You will get favorable cases after choosing 3 balls from 9 white balls and you can do this by 9C3 ways. You will obtain the total number of results after selecting 4 balls from 15 balls and you can also do in 15 C3 ways. The needed probability is 9 C3 / 15 C3.

In these worksheets, your students will determine the number of combinations that are possible for a given situation. They will find combinations by selecting for specific information. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. It also includes ample worksheets for students to practice independently. Worksheets are provided at both the basic and intermediate skills levels. When finished with this set of worksheets, students will be able to both find and create combinations that meet specified criteria. These worksheets explain how to determine the number of combinations that are possible for a given situation. Sample problems are solved and practice problems are provided.

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Combination Probability Worksheets

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Combinations Lesson and Practice

We walk you through the explanation of this problem: In how many ways can a cricket team of eleven people be chosen out of a batch of 15 players?

Lesson and Practice

A sample problem is solved and two practice problems are provided. The sample problem is: Out of 7 consonants and 4 vowels, how many ways can 3 consonants and 2 vowels be picked?

Worksheet

Students will determine the number of combinations that are possible for a given situation. Ten problems are provided.

Practice

Example problem: 5 A box contains 1 white ball, 2 blue balls, and 4 red balls. In how many ways can 2 balls be drawn from the box, if at least one blue ball is to be included in the draw?

Drill

You will solve exercises like this: From a group of 7 men and 6 women, five people are going to be selected to a committee; so that at least 3 men are there on the committee. In how many ways could it be done?

Warmup

Here are three problems you can work on as a class.

Working with Combinations Worksheet

Students will find the number of possible combinations in selecting for the information provided. Ten problems are provided.

Class Worksheet

You will attempt problems like this: There are 12 cans in a garbage can. How many ways can you pick 6 cans from the garbage can at once?

Review Page 1

The concept of how to find the number of different possible combinations is reviewed. A sample problem is solved.

Review Page 2

You will tackle real world problems like: There are 10 things in a box. How many ways can you pick 4 things from the box at once?

Quiz

Students will demonstrate their proficiency will solving combination based problems. Ten problems are provided.

Check

You will work through this different series of problems. Example: There are 15 rocks in a sack. How many ways can you pick 10 rocks from the sack at once?

Lesson

We walk you step by step through this problem: On the bookshelf, there are 5 Math books, 7 History books and 7 Chemistry books. If three books are selected randomly without replacement, what is the probability of getting 2 Math books and 1 History book?

Introduction to Combinations Worksheet

Students will find the possible number of different combinations that are presented in each scenario. Ten problems are provided.

Practice

These are some really out there problems.

Review and Practice

A Middle School has 20 students, 7 girls and 8 boys and 5 teachers. If five people are selected randomly.

Quiz

Students will demonstrate their ability to find the possible types of combinations that are present. Ten problems are provided.

Check

Students will find the indicated possible combinations. Three problems are provided, and space is included for students to copy the correct answer when given.

Combinations Basic Skills Worksheet

Example: There are thirteen shirts of different colors in a cupboard. How many ways are possible to choose four shirts from the cupboard?

Practice

Students will practice using basic skills to find the combinations. Ten problems are provided.

Worksheet

Students will use intermediate skills to find the helping of possible combinations. Ten problems are provided.

Combinations Intermediate Skills Practice

Exercises that include: There are 24 students in a class. Find the number of combinations possible to select a team of 4 students to work on a group project.

Drill

Students will find the combinations in these intermediate-level problems. Example: There are 21 students in a class. Find the number of combinations possible to select a team of 7 students to work on a group project.