Combination solver
Step by step worksheet, combination

Solve combination in this form \[^nC_r=\frac{n!}{r!\left(n-r\right)!} \]

combination solver calculator

The combination solver is an easy-to-use, free, and open source math solver that calculates the total number of combinations, number of possible arrangements in a collection of items, and the number of solutions with particular values.
Solves combination using the formula below.
Where n = total number of objects in the set, and r = number of choosing objects from the set.


Solve C(9, 5)

Step 1

Enter 9 into box marked "n" and 5 into the box marked "r"


Hit the check mark to solve combination.

About Combination Solver Calculator

A combination is the number of selections of different items from distinguishable items when order of selection is ignored.

In algebra, combinations refer to the selection of a group of objects from a larger set, where the order of the objects does not matter. The number of combinations can be found using the formula:

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

where n represents the total number of objects and r represents the number of objects being selected.

combination formula

Applications of Combination in Various Fields Include

  • 1. Probability: Combinations are used to calculate the number of favorable outcomes in an event. For example, determining the number of possible outcomes in a game of poker or in rolling dice.

  • 2. Genetics: Combinations are used in genetics to calculate the possible combinations of genes and alleles in the offspring.

  • 3. Combinatorial optimization: Combinations are used to solve optimization problems, such as finding the most efficient route for delivery trucks to visit multiple locations.

  • 4. Combinatorics: Combinations are a fundamental concept in combinatorics, which studies the arrangement and selection of objects.

  • 5. Data analysis: Combinations are used in data analysis to calculate the number of possible subsets or combinations of variables, which can provide insights into patterns and relationships in the data.

  • 6. Cryptography: Combinations are used in cryptography to generate secure passwords or encryption keys by randomly selecting combinations of characters or numbers.

  • 7. Computer science: Combinations are used in algorithms and data structures, such as generating permutations or subsets of a set.

  • 8. Game theory: Combinations are used in game theory to analyze the possible combinations of strategies and outcomes in games.

Examples of Combination:

C(8, 4)

  • C(8, 4) = 8! / (4!(8 - 4)!)
    = 8! / (4! 4!)

  • We can simplify this expression as:

  • 8! = 8 x 7 x 6 x 5 x 4! = 8 7 6 5 4

  • 4! = 4 x 3 x 2 x 1

  • Substituting these values back into the formula:

  • C(8, 4) = (8 x 7 x 6 x 5 x 4) / (4 x 3 x 2 x 1)

  • This can be further simplified as:

  • C(8, 4) = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1)

C(8, 4) = 70

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