Combinations Without Replacement Calculator: Calculate Possible Combinations

Welcome to our Combinations Without Replacement Calculator, an essential tool to help you quickly calculate the number of ways to select a subset from a larger set of items, where order does not matter, and each item can only be selected once.

What Are Combinations Without Replacement?

Combinations without replacement refer to selecting a group of items from a larger set, where:

• The order in which items are selected does not matter.
• An item can only be chosen once (no repetitions).

In other words, you are selecting distinct items without regard to the order they are chosen. For example, if you want to select 3 books from a set of 5 books, the selection {Book 1, Book 2, Book 3} is the same as {Book 3, Book 2, Book 1}.

The Formula for Combinations Without Replacement

The formula for calculating combinations without replacement is:

C(n,r) = n! / (r! * (n - r)!)

Where:

• n is the total number of items in the set.
• r is the number of items you want to choose from the set.
• n! denotes the factorial of n (which is the product of all positive integers up to n).

Example of Combinations Without Replacement

Let’s say you have 5 different colored balls and you want to choose 3 of them. The total number of possible combinations can be calculated using the formulaAll Calculator:

C(5,3) = 5! / (3! * (5 - 3)!) = 10

How to Use the Combinations Without Replacement Calculator

• Enter the Total Number of Items (n): This is the size of the set you are choosing from.
• Enter the Number of Items to Choose (r): This is the size of the subset you want to select.
• Click 'Calculate': Get the result instantly, showing you the total number of possible combinations.

Try Our Combinations Without Replacement Calculator Now!

Simply enter your numbers in the input fields, and click "Calculate" to see the number of possible combinations. Our Combinations Without Replacement Calculator is fast, free, and easy to use.