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🎲 Binomial & Combinatorics Calculator

Compute combinations (nCr), permutations (nPr), and binomial probabilities P(X=k), P(X≤k), and P(X≥k) for discrete probability questions.

Binomial & Combinatorics Calculator

Compute nCr combinations, nPr permutations, and binomial probabilities P(X = k), P(X ≤ k), and P(X ≥ k). Perfect for discrete probability questions and combinatorics homework.

Combinations & permutations

n (items)

r (chosen)

Combinations nCr

120

Permutations nPr

720

nCr calculatorcombinations and permutations calculator

Binomial probabilities

Number of trials (n)

Probability of success (p)Enter as a decimal between 0 and 1.

Number of successes (k)

P(X = k)

0.266828

P(X ≤ k)

0.649611

P(X ≥ k)

0.617217

How to use this tool

Use the top card to compute nCr combinations and nPr permutations from integers n and r.
Enter n, p, and k in the binomial panel to compute binomial probabilities.
Interpret P(X = k), P(X ≤ k), and P(X ≥ k) in the context of your probability question.

Binomial probability calculator for quick checks

Avoid manual binomial coefficient calculations when checking exam answers.
Use nCr as a combinations calculator and nPr as a permutations calculator.
See exact, cumulative, and at‑least probabilities for the binomial distribution.

What this binomial calculator assumes

Trials are independent with a constant probability of success p.
The random variable X counts the number of successes in n trials.
Probabilities are computed directly from the binomial formula with combinations nCr.

FAQ

What is the difference between combinations (nCr) and permutations (nPr)?: Combinations nCr count selections where order does not matter. Permutations nPr count ordered arrangements of r items from n.
Can I enter percentages for p instead of decimals?: Enter p as a decimal between 0 and 1 (for example, 0.3 instead of 30%). This keeps the binomial formula consistent.
Why do very extreme probabilities show as 0?: For large n or very small probabilities, rounding to 6 decimal places may show tiny probabilities as 0. The underlying calculation still uses full floating‑point precision.

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