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The Combinations Calculator will find the number of possible combinations that can be obtained by taking a sub-set of items from a larger set. Basically, it shows how many different possible sub-sets can be made from the larger set. For this calculator, the order of the items chosen in the sub-set does not matter.

Calculate the combinations for C(n,r) = n! / ( r!(n - r)! ). For 0 <= r <= n.

“n choose r” = C(n,r) = n! / ( r! (n - r)! )

The formula shows the number of ways a sample of “r” elements can be obtained from a larger set of “n” distinguishable objects where order does not count and repetitions are not allowed. [1] "The number of ways of picking r unordered outcomes from n possibilities." [2]

Also referred to as r-combination or "n choose r". In some resources the notation uses k instead of r so you may see these referred to as k-combination or "n choose k".

**Combination Problem 1****:** A teacher is going to choose 3 students from her class to compete in the spelling bee. She wants to figure out how many unique teams of 3 can be created from her class of 25.

In this example, we are taking a sub-set of 3 students (r) from a larger set of 25 students (n). Looking at the formula, we must calculate “25 choose 3”

C (25,3)= 25!/(3! * (25-3)!)= **2,300 Possible Teams**

**Combination Problem 2****:** A restaurant asks some of its frequent customers to choose their favorite 4 items on the menu. If the menu has 18 items to choose from, how many different answers could the customers give?

Here we take a 4 item sub-set (r) from the larger 18 item menu (n). Therefore, we must simply find “18 Choose 4”

C (18,4)= 18!/(4! * (18-4)!)= **3,060 Possible Answers**

[1] Zwillinger, Daniel (Editor-in-Chief). *CRC Standard Mathematical Tables and Formulae, 31st Edition* New York, NY: CRC Press, p. 206, 2003.

For more information on combinations and binomial coefficients please see http://mathworld.wolfram.com/Combination.html

**Cite this content, page or calculator as:**

Furey, Edward "Combinations Calculator (nCr)" From *http://www.CalculatorSoup.com* - Online Calculator Resource.