calculation of binomial coefficients
Calculation of binomial coefficients
A binomial coefficient calculator that allows you to calculate a binomial coefficient from two integers.
Definition of the binomial coefficient
In mathematics, the binomial coefficient of two integers n and k is the number `(n!)/(k!(n-k)!`, with `k<=n`. This number can be noted `((n),(k))` or `C_n^k`.
Binomial Coefficient Calculator
The binomial coefficient calculator allows you to calculate a binomial coefficient from two integers. To calculate the binomial coefficient of two numbers n and k, the calculator uses the following formula: `(n!)/(k!(n-k)!`. The steps of the calculation are specified.
For example, to calculate the binomial coefficient of the following two integers 5 and 3, simply enter binomial_coefficient(`5;3`), and the calculator returns the result, which is 10.
The binomial coefficients intervene in particular in the expansion of algebraic expression with Newton's binomial formula or in probability with combinatorics or combinations. One of the specific features of the binomial coefficients calculator is to indicate the different calculation steps that allow to find the result.
Syntax :
binomial_coefficient(n;k), n and k are integers.
Examples :
binomial_coefficient(5;3), returns 10
- Number of arrangement of a set calculator : arrangement. To calculate online the number of arrangement of p elements of a set of n elements.
- Calculation of binomial coefficients : binomial_coefficient. A binomial coefficient calculator that allows you to calculate a binomial coefficient from two integers.
- To count the number of combinations : combination. To calculate the number of k elements of part of a set of n elements.
- Base-n converter : base_converter. The calculator allows you to make decimal, binary, hexadecimal conversions, and more generally to any base n between 2 and 36.
- Prime factorization calculator : prime_factorization. The function prime_factorization is used to calculate online the decomposition of an integer into prime factors.
- Quotient and remainder calculator : euclidean_division. The calculator allows to find online the quotient and the remainder in the euclidean division of two polynomials or two integers.
- Parity of a number : is_odd. Is_odd function returns true if the number passed is odd, false otherwise.
- Parity of a number : is_even. Is_even function returns 1 if the number is even, 0 otherwise.
- Factorial calculator : factorial. The factorial of a natural number n is the product of the positive integers less than or equal to n. The factorial calculator allows you to find this number.
- Integer calculations : integer_functions. This calculator allows you to apply special functions to an integer: prime_factorization, base_converter, factorial, percentage, permutation, perimeter, is_even, is_odd.
- Permutation calculator : permutation. To calculate online the number of permutation of a set of n elements.
- Gcd calculation online : gcd. GCD calculator that uses Euclid's algorithm to give the steps of the GCD calculation.
- Least common multiple : lcm. LCM calculator to calculate the least common multiple (LCM).
- Pythagorean theorem calculator : pythagorean. The calculator uses the Pythagorean theorem to verify that a triangle is right-angled or to find the length of one side of a right-angled triangle.
- Countdown solver : arithmetic_solver. This countdown solver allows finding a target number from a set of integer in using arithmetic operations.