Binomial Coefficient Calculator
Use our binomial coefficient calculator to calculate binomial coefficient values (n choose k) instantly. Includes how to calculate binomial coefficient, how to do binomial coefficient on calculator, how to put binomial coefficient in calculator, TI-84 steps, and binomial coefficient statistics context.
What is a Binomial Coefficient?
A binomial coefficient counts how many ways you can choose k items from n items without regard to order. It’s written as “n choose k” and commonly shown as C(n, k) or (n k).
Binomial coefficients appear in the binomial theorem, combinations, Pascal’s triangle, and binomial coefficient statistics (like binomial probability and combinatorics in statistics).
This binomial coefficient calculator computes C(n, k) quickly using the standard factorial-based formula.
Binomial Coefficient Formula
The binomial coefficient (n choose k) is a combinations formula. It can be computed using factorials or using an equivalent product form for efficiency.
Valid for integers n ≥ 0 and 0 ≤ k ≤ n.
Choosing k is the same as choosing what you leave out.
There are 10 ways to choose 2 items from 5.
Sometimes it’s easier to compute with the smaller k.
How to Use the Binomial Coefficient Calculator
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Enter n (the total number of items).
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Enter k (the number of items you choose).
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The calculator computes C(n, k) using the binomial coefficient formula.
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Use the result for combinations, binomial expansions, or binomial coefficient statistics problems.
Frequently Asked Questions
Use C(n, k) = n! / (k!(n−k)!).
It counts combinations and appears in binomial probability formulas and combinatorics used in statistics.
Many scientific calculators have an nCr function. Enter n, choose nCr, then enter k.
Use the combinations function nCr (sometimes under a PRB or probability menu). It computes n choose k.
On TI-84, nCr is typically in the MATH menu under PRB. Enter n, select nCr, then enter k.
For standard combinations, C(n, k) is defined as 0 when k > n, because you can’t choose more items than you have.
No. Binomial coefficients count combinations (order doesn’t matter). Permutations count ordered arrangements.