Aug 1, 2025 · The Combinations Calculator will find the number of possible combinations that can be obtained by taking a sample of items from a larger set. Basically, it shows how many different …

For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an …

Jul 23, 2025 · The number of all such combinations is calculated by the combinations formula: nCr or C (n, r). Example: All the combinations of four different objects a, b, c, d taken two at a time are ab, ac, …

What Is Combinations Formula? The combinations formula is used to easily find the number of possible different groups of r objects each, which can be formed from the available n different objects.

The formula for combinations, also known as binomial coefficients, is represented as nCr, where n is the total number of objects and r is the number of objects to be chosen.

In English we use the word combination loosely, without thinking if the order of things is important. In other words:

Scroll down the page for more examples and solutions on how to use the combination formula. The number of combinations of selecting k items from a set of n distinct items is denoted in various ways:

This is just one example of using combinations in probability. There are many other ways that combinations can be used as part of more complex probability calculations.

Explore the concept of combination in mathematics. Learn combination formulas, solve examples with answers, and understand combinations with and without repetition for exams like JEE.

The Combination formula in Maths shows the number of ways a given sample of “k” elements can be obtained from a larger set of “n” distinguishable numbers of objects.