Given **n** and **m**, the task is to find the number of permutations of **n** distinct things taking them all at a time such that **m** particular things never come together.**Examples:**

Input :7, 3Output :420Input :9, 2Output :282240

**Approach:****Derivation of the formula – **

Total number of arrangements possible using n distinct objects taking all at a time =

Number of arrangements of n distinct things taking all at a time, when m particular things always come together, is

Hence, the number of permutations of distinct things taking all at a time, when particular things never come together –

Permutations = n! - (n-m+1)! × m!

**Below is the Python implementation of above approach – **

## C++

`#include<bits/stdc++.h>` `using` `namespace` `std;` `int` `factorial(` `int` `n)` `{` ` ` `int` `fact = 1;` ` ` `for` `(` `int` `i = 2; i <= n; i++)` ` ` `fact = fact * i ;` ` ` `return` `(fact);` `}` `int` `result(` `int` `n, ` `int` `m)` `{` ` ` `return` `(factorial(n) - ` ` ` `factorial(n - m + 1) *` ` ` `factorial(m));` `}` `// Driver Code` `int` `main()` `{` ` ` `cout(result(5, 3));` `}` `// This code is contributed by Mohit Kumar` |

## Java

`class` `GFG` `{` `static` `int` `factorial(` `int` `n)` `{` ` ` `int` `fact = ` `1` `;` ` ` `for` `(` `int` `i = ` `2` `; i <= n; i++)` ` ` `fact = fact * i ;` ` ` `return` `(fact);` `}` `static` `int` `result(` `int` `n, ` `int` `m)` `{` ` ` `return` `(factorial(n) -` ` ` `factorial(n - m + ` `1` `) *` ` ` `factorial(m));` `}` `// Driver Code` `public` `static` `void` `main(String args[])` `{` ` ` `System.out.println(result(` `5` `, ` `3` `));` `}` `}` `// This code is contributed by Arnab Kundu` |

## Python3

`def` `factorial(n):` ` ` `fact ` `=` `1` `;` ` ` `for` `i ` `in` `range` `(` `2` `, n ` `+` `1` `):` ` ` `fact ` `=` `fact ` `*` `i` ` ` `return` `(fact)` `def` `result(n, m):` ` ` `return` `(factorial(n) ` `-` `factorial(n ` `-` `m ` `+` `1` `) ` `*` `factorial(m))` `# driver code` `print` `(result(` `5` `, ` `3` `))` |

## C#

`using` `System;` `class` `GFG` `{` ` ` `static` `int` `factorial(` `int` `n)` ` ` `{` ` ` `int` `fact = 1;` ` ` `for` `(` `int` `i = 2; i <= n; i++)` ` ` `fact = fact * i ;` ` ` `return` `(fact);` ` ` `}` ` ` ` ` `static` `int` `result(` `int` `n, ` `int` `m)` ` ` `{` ` ` `return` `(factorial(n) -` ` ` `factorial(n - m + 1) *` ` ` `factorial(m));` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `Console.WriteLine(result(5, 3));` ` ` `}` `}` `// This code is contributed by AnkitRai01` |

## Javascript

`<script>` `// Below is the JavaScript implementation of above approach` `function` `factorial(n)` `{` ` ` `let fact = 1;` ` ` `for` `(let i = 2; i <= n; i++)` ` ` `fact = fact * i ;` ` ` `return` `(fact);` `}` `function` `result(n, m)` `{` ` ` `return` `(factorial(n) -` ` ` `factorial(n - m + 1) *` ` ` `factorial(m));` `}` `// Driver Code` `document.write(result(5, 3));` `// This code is contributed by Surbhi Tyagi.` `</script>` |

**Output : **

84

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