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About

Understanding probability and statistics is fundamental to fields ranging from data science to risk management. However, the formulas for counting principles like Permutations and Combinations can be confusing for students. This tool serves as both a calculator and a tutor.

Instead of simply outputting a number, it breaks down the 'working out' process. Whether you are calculating how many ways to arrange a deck of cards (Permutations) or how many lottery teams can be picked from a group (Combinations), this tool visualizes the factorials and fractions involved. It also includes a suite for basic set theory probability, handling unions and intersections of events.

permutations calculator combinations nCr probability A or B statistics solver nPr calculator

Formulas

The foundation of counting is the Factorial:

n! = n × (n 1) × ... × 1

For probability of two independent events A and B occurring together:

P(A B) = P(A) × P(B)

For mutually exclusive events A or B:

P(A B) = P(A) + P(B)

Reference Data

FunctionFormulaDescription
Factorial
n!
Product of all positive integers ≤ n.
Permutation (Order matters)
nPr = n!(nr)!
Arranging r items from n distinct items.
Combination (Order doesn't matter)
nCr = n!r!(nr)!
Selecting r items from n distinct items.
Union of Events
P(A B)
Probability of A OR B occurring.
Intersection
P(A B)
Probability of A AND B occurring.

Frequently Asked Questions

The key difference is order. In a Permutation, the order of arrangement matters (e.g., a combination lock code 1-2-3 is different from 3-2-1). In a Combination, order does not matter (e.g., selecting 3 distinct fruits for a salad; apple-banana-cherry is the same as cherry-apple-banana).
No. Probability is always a number between 0 (impossible) and 1 (certain). If a calculation results in a number greater than 1, check your inputs; you may have summed non-mutually exclusive probabilities without subtracting the intersection.
'n' represents the total number of items in the set, and 'r' represents the number of items you are choosing or arranging from that set.