Scientific Calculator: Combinatorics





Scientific Calculator: Combinatorics


Content

Factorial
Permutations
Permutations of k objects
Combinations







Factorial

In mathematics, the factorial of a natural number, denoted by n!, is the product of all natural numbers smaller or equal to n.



This can also be written as:


By convention, 0! = 1.
Example:






Permutations

In mathematics, a permutation of a set of objects is defined as a particular order of the items.
For example, the permutations of the set {1, 2, 3} are: (1, 2, 3); (1, 3, 2); (2, 1, 3); (2, 3, 1); (3, 1, 2); (3, 2, 1);

The number of permutations for a set is given by n!.





Permutations of k objects

Example: the permutations of 2 items from the set {1, 2, 3} are:
(1, 2); (2, 1); (1, 3); (3, 1); (2, 3); (3, 2);

The number of permutations of k objects is given by the formula:

After making the simplifications, we get:






Combinations

In mathematics, a combination is a method of selecting a number of objects from a larger set, where order doesn't matter.

For example, the combinations of 2 items from the set {1, 2, 3} are:
{1, 2}; {1, 3}; {2, 3};

The number of combinations is given by the formula:

After making the simplifications, we get:







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