# BigIntegerMath binomial() function | Guava | Java

The binomial(int n, int k) method of Guava’s BigIntegerMath class returns n choose k, also known as the binomial coefficient of n and k, that is,
`n! / (k! (n - k)!)`
Syntax:
```public static BigInteger binomial(int n, int k)
```
Parameters: This method takes the following parameters:
• n: The base for binomial expansion.
• k: The power for binomial expansion.
Return Value: This method returns the binomial coefficient of n and k. Exceptions: This method throws IllegalArgumentException if n < 0, k < 0 or k > n. Note: The result can take as much as O(k log n) space. Below examples illustrates the BigIntegerMath.binomial() method: Example 1:
 `// Java code to show implementation of ``// binomial(int n, int k) method ``// of Guava's BigIntegerMath class `` ` `import` `java.math.*; ``import` `com.google.common.math.BigIntegerMath; `` ` `class` `GFG { `` ` `    ``// Driver code ``    ``public` `static` `void` `main(String args[]) ``    ``{ ``        ``int` `n = ``5``; ``        ``int` `k = ``2``; `` ` `        ``// Using binomial(int n, int k) method of ``        ``// Guava's BigIntegerMath class ``        ``BigInteger ans = BigIntegerMath.binomial(n, k); `` ` `        ``System.out.println(``"Binomial Coefficient of "``                           ``+ n + ``" & "` `+ k ``                           ``+ ``" is: "` `+ ans); `` ` `        ``int` `n1 = ``15``; ``        ``int` `k1 = ``9``; `` ` `        ``// Using binomial(int n, int k) method of ``        ``// Guava's BigIntegerMath class ``        ``BigInteger ans1 = BigIntegerMath.binomial(n1, k1); `` ` `        ``System.out.println(``"Binomial Coefficient of "``                           ``+ n1 + ``" & "` `+ k1 ``                           ``+ ``" is: "` `+ ans1); ``    ``} ``} `

Output:
```Binomial Coefficient of 5 & 2 is: 10
Binomial Coefficient of 15 & 9 is: 5005
```
Example 2:
 `// Java code to show implementation of ``// binomial(int n, int k) method ``// of Guava's BigIntegerMath class `` ` `import` `java.math.*; ``import` `com.google.common.math.BigIntegerMath; `` ` `class` `GFG { `` ` `    ``// Driver code ``    ``public` `static` `void` `main(String args[]) ``    ``{ `` ` `        ``try` `{ ``            ``int` `n = ``5``; ``            ``int` `k = ``7``; `` ` `            ``// Using binomial(int n, int k) method of ``            ``// Guava's BigIntegerMath class ``            ``// This should raise "IllegalArgumentException" ``            ``// as k > n ``            ``BigInteger ans = BigIntegerMath.binomial(n, k); `` ` `            ``System.out.println(``"Binomial Coefficient of"``                               ``+ n + ``" & "` `+ k ``                               ``+ ``" is: "` `+ ans); ``        ``} ``        ``catch` `(Exception e) { ``            ``System.out.println(``"Exception: "` `+ e); ``        ``} ``    ``} ``} `

Output:
```Exception: java.lang.IllegalArgumentException: k (7) > n (5)
```