Binomial Coefficient Calculator
This calculator computes the binomial coefficient (also known as “n choose k”), which represents the number of ways to choose k elements from a set of n without regard to order. It’s widely used in combinatorics, probability, and the binomial theorem.
Calculate “n Choose k” Combinations
Binomial Coefficient Formula
$$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$
Explanation:
The binomial coefficient gives the number of combinations of k elements from a set of n, calculated using factorials. It appears in Pascal’s Triangle and the expansion of $$(a + b)^n$$.
Binomial Coefficient – Calculation Example
n = 5, k = 2
- 5! = 120
- 2! = 2, (5 – 2)! = 6
- 120 / (2 × 6) = 120 / 12 = 10
Result: 5 choose 2 = 10
Binomial coefficients are essential in combinatorics (counting problems), algebra (binomial expansions), and probability (calculating likelihood of outcomes). They are symmetric and appear in various identities like Pascal’s Rule. This calculator is great for math students, educators, and researchers.