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Getting binomial coefficient of a number in Julia – binomial() Method

  • Last Updated : 21 Apr, 2020

The binomial() is an inbuilt function in julia which is used to return the binomial coefficient $\binom{n}{k}$ which is the coefficient of the kth term in the polynomial expansion of $(1+x)^n$.
Its formula is –

    \[\binom{n}{k} = \frac{n!}{k! (n-k)!}\]

, where $n!$ is the factorial of n.
If n is negative, then it is defined in terms of the identity

    \[\binom{n}{k} = (-1)^k \binom{k-n-1}{k}\]

.



Syntax: binomial(n::Integer, k::Integer)

Parameters:

  • n: Specified number
  • k: Specified number

Returns: It returns the binomial coefficient $\binom{n}{k}$.

Example 1:




# Julia program to illustrate 
# the use of binomial() method
  
# Getting the binomial coefficient
println(binomial(6, 4))
println(factorial(6) รท (factorial(6-4) * factorial(4)))

Output:

15
15

Example 2:




# Julia program to illustrate 
# the use of binomial() method
  
# Getting the binomial coefficient
println(binomial(6, 3))
println(binomial(-6, 3))
println(binomial(-6, -2))
println(binomial(5, 2))

Output:

20
-56
0
10



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