Input n, k (0 ≤ k ≤ n ≤ 50000) |
Result: C(n,k) (to select: click, Ctrl+A, Ctrl+C)
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Run time: |
The binomial coefficient C(n,k)
is defined as the number of different ways to choose a k-element subset from an n-element set.
The values C(n,k) appear in
Pascal's triangle and satisfy the recurrence
C(n,k) =
C(n − 1, k − 1) + C(n − 1, k).
Equivalently, C(n,k) is the coefficient of the akbn−k
term in the full expansion of the binomial power (a + b)n.
Note that in the expression (a + b)n the variables a and b appear in a symmetric manner;
therefore, we have C(n,k) = C(n, n−k) for any
k ≤ n.
For example, the expansion
(a + b)4 =
a4 + 4a3b + 6a2b2 + 4ab3 + b4
yields the following binomial coefficients:
C(4,0) = 1,
C(4,1) = 4,
C(4,2) = 6,
C(4,3) = 4,
C(4,4) = 1.
This online calculator computes binomial coefficients C(n,k)
for input values 0 ≤ k ≤ n ≤ 50000 in arbitrary precision arithmetic.
So, for instance, you will get all digits of C(9000,4500) –
all the 2708 digits of this very large number!
See also:
• 100+ digit calculator: arbitrary precision arithmetic
• Prime factorization calculator
• Euler's totient function φ calculator
• Highly composite numbers
• Divisors and sum-of-divisors calculator
• Fibonacci numbers calculator
• Catalan numbers calculator
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Doing Math with JavaScript