# Program for Binomial Coefficients table

Given an integer max, print Binomial Coefficients table that prints all binomial coefficients B(m, x) where m and x vary from 0 to max

Example :

```Input : max = 3
Output :
0   1
1   1   1
2   1   2   1
3   1   3   3   1
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The easiest way to explain what binomial coefficients are is to say that they count certain ways of grouping items. Specifically, the binomial coefficient B(m, x) counts the number of ways to form an unordered collection of k items chosen from a collection of n distinct items.
Binomial coefficients are used in the study of binomial distributions and multicomponent redundant systems. It is given by

Example :

```Compute B(7, 3)  where m = 7 and x = 1
(7!/3!(7-3)!)7
= 7!/3!*4!
= (7*6*5*4*3*2*1)/(3*2*1)*(4*3*2*1)
= 35
```

A table of binomial coefficients is required to determine the binomial coefficient for any value m and x.

Problem Analysis :
The binomial coefficient can be recursively calculated as follows –
further,

That is the binomial coefficient is one when either x is zero or m is zero. The program prints the table of binomial coefficients for .

## C++

 `// C++ program for binomial coefficients ` `#include ` ` `  `// Function to print binomial table ` `int` `printbinomial(``int` `max) ` `{ ` `    ``for` `(``int` `m = 0; m <= max; m++) { ` `        ``printf``(``"%2d"``, m); ` `        ``int` `binom = 1; ` `        ``for` `(``int` `x = 0; x <= m; x++) { ` ` `  `            ``// B(m, x) is 1 if either m or x is ` `            ``// is 0. ` `            ``if` `(m != 0 && x != 0) ` ` `  `                ``// Otherwise using recursive formula ` `                ``// B(m, x) = B(m, x - 1) * (m - x + 1) / x ` `                ``binom = binom * (m - x + 1) / x; ` ` `  `            ``printf``(``"%4d"``, binom); ` `        ``} ` `        ``printf``(``"\n"``); ` `    ``} ` `} ` ` `  `// Driver Function ` `int` `main() ` `{ ` `    ``int` `max = 10; ` `    ``printbinomial(max); ` `    ``return` `0; ` `} `

## Java

 `// Java program for  ` `// binomial coefficients ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `     `  `// Function to print  ` `// binomial table ` `static` `void` `printbinomial(``int` `max) ` `{ ` `    ``for` `(``int` `m = ``0``; m <= max; m++) ` `    ``{ ` `        ``System.out.print(m + ``" "``); ` `        ``int` `binom = ``1``; ` `        ``for` `(``int` `x = ``0``; x <= m; x++)  ` `        ``{ ` ` `  `            ``// B(m, x) is 1 if either  ` `            ``// m or x is is 0. ` `            ``if` `(m != ``0` `&& x != ``0``) ` ` `  `                ``// Otherwise using  ` `                ``// recursive formula ` `                ``// B(m, x) = B(m, x - 1) *  ` `                ``//            (m - x + 1) / x ` `                ``binom = binom * (m - x + ``1``) / x; ` ` `  `            ``System.out.print(binom + ``" "``); ` `        ``} ` `        ``System.out.println(); ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main (String[] args)  ` `{ ` `    ``int` `max = ``10``; ` `    ``printbinomial(max); ` `} ` `} ` ` `  `// This code is contributed ` `// by akt_mit `

## Python3

 `# Python3 program for binomial ` `# coefficients ` ` `  `# Function to print binomial table ` `def` `printbinomial (``max``): ` `     `  `    ``for` `m ``in` `range``(``max` `+` `1``): ` `        ``print``( ``'% 2d'``%` `m, end ``=` `' '``) ` `        ``binom ``=` `1` `        ``for` `x ``in` `range``(m ``+` `1``): ` `             `  `            ``# B(m, x) is 1 if either m  ` `            ``# or x is is 0. ` `            ``if` `m !``=` `0` `and` `x !``=` `0``: ` `                 `  `                ``# Otherwise using recursive ` `                ``# formula ` `                ``# B(m, x) = B(m, x - 1) * ` `                ``#           (m - x + 1) / x ` `                ``binom ``=` `binom ``*` `(m ``-` `x ``+` `1``) ``/` `x ` `            ``print``( ``'% 4d'``%` `binom, end ``=` `' '``) ` `        ``print``(``"\n"``, end ``=` `'') ` `         `  `# Driver Function ` `max` `=` `10` `printbinomial(``max``) ` ` `  `# This code is contributed by "Sharad_bhardwaj". `

## C#

 `// C# program for binomial coefficients ` `using` `System; ` ` `  `public` `class` `GFG { ` ` `  `    ``// Function to print binomial table ` `    ``static` `void` `printbinomial(``int` `max) ` `    ``{ ` `        ``for` `(``int` `m = 0; m <= max; m++) { ` `            ``Console.Write(m + ``" "``); ` `            ``int` `binom = 1; ` `            ``for` `(``int` `x = 0; x <= m; x++) { ` ` `  `                ``// B(m, x) is 1 if either m ` `                ``// or x is is 0. ` `                ``if` `(m != 0 && x != 0) ` ` `  `                    ``// Otherwise using recursive formula ` `                    ``// B(m, x) = B(m, x - 1) * (m - x + 1) / x ` `                    ``binom = binom * (m - x + 1) / x; ` ` `  `                ``Console.Write(binom + ``" "``); ` `            ``} ` `            ``Console.WriteLine(); ` `        ``} ` `    ``} ` ` `  `    ``// Driver Function ` `    ``static` `public` `void` `Main() ` `    ``{ ` `        ``int` `max = 10; ` `        ``printbinomial(max); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output :

``` 0   1
1   1   1
2   1   2   1
3   1   3   3   1
4   1   4   6   4   1
5   1   5  10  10   5   1
6   1   6  15  20  15   6   1
7   1   7  21  35  35  21   7   1
8   1   8  28  56  70  56  28   8   1
9   1   9  36  84 126 126  84  36   9   1
10   1  10  45 120 210 252 210 120  45  10   1
```

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