Permutation & Combination Calculator pro version

Permutation & Combination Calculator

Calculate permutations and combinations with ease

Total number of objects (n):

Number of objects selected (r):

Permutation (nPr)

Combination (nCr)

Result

0

Permutation: Definition & Usage

Definition: A permutation is an arrangement of objects in a specific order. The order of arrangement matters in permutation.

nPr = n! / (n - r)!
where n is the total number of objects,
r is the number of objects selected,
and ! denotes factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1 = 120)

How to calculate: To calculate the number of permutations of r objects from a set of n objects, use the formula nPr = n! / (n - r)!. This formula accounts for the different orders in which objects can be arranged.

Where Permutation is Used:

• Password combinations: Calculating possible sequences of characters
• Race rankings: Determining possible outcomes of races
• Seating arrangements: Arranging people in specific orders
• Cryptography: Creating secure encryption algorithms
• Game strategies: Analyzing possible moves in games
• Statistics: Calculating probabilities of ordered events

Combination: Definition & Usage

Definition: A combination is a selection of items where order does not matter. It's about choosing items from a collection.

nCr = n! / (r! * (n - r)!)
where n is the total number of objects,
r is the number of objects selected,
and ! denotes factorial

How to calculate: To calculate the number of combinations of r objects from a set of n objects, use the formula nCr = n! / (r! * (n - r)!). This formula does not account for different orders of the same items.

Where Combination is Used:

• Lottery probabilities: Calculating chances of winning
• Committee formation: Selecting members for a group
• Card games: Determining possible hands
• Product selection: Choosing items from a catalog
• Research sampling: Selecting participants for studies
• Menu combinations: Creating meal options from ingredients