# Count of distinct permutations of every possible length of given string

• Difficulty Level : Basic
• Last Updated : 29 Apr, 2021

Given a string S, the task is to count the distinct permutations of every possible length of the given string.

Note: Repetition of characters is not allowed in the string.

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Input: S = “abc”
Output: 15
Explanation:
Possible Permutations of every length are:
{“a”, “b”, “c”, “ab”, “bc”, “ac”, “ba”, “ca”, “cb”, “abc”, “acb”, “bac”, “bca”, “cab”, “cba”}

Input: S = “xz”
Output: 4

Approach: The idea is to find the count of combinations of every possible length of the string and their sum is the total number of distinct permutations possible of different lengths. Therefore, for N length string total number of distinct permutation of different length is:

Total Combinations possible: nP1 + nP2 + nP3 + nP4 + …… + nPn

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the``// above approach` `#include ``#include ``using` `namespace` `std;` `// Function to find the factorial``// of a number``int` `fact(``int` `a)``{``    ``int` `i, f = 1;` `    ``// Loop to find the factorial``    ``// of the given number``    ``for` `(i = 2; i <= a; i++)``        ``f = f * i;``    ``return` `f;``}` `// Function to find the number``// of permutations possible``// for a given string``int` `permute(``int` `n, ``int` `r)``{``    ``int` `ans = 0;``    ``ans = (fact(n) / fact(n - r));``    ``return` `ans;``}` `// Function to find the total``// number of combinations possible``int` `findPermutations(``int` `n)``{``    ``int` `sum = 0, P;``    ``for` `(``int` `r = 1; r <= n; r++) {``        ``P = permute(n, r);``        ``sum = sum + P;``    ``}``    ``return` `sum;``}` `// Driver Code``int` `main()``{``    ``string str = ``"xz"``;``    ``int` `result, n;``    ``n = str.length();` `    ``cout << findPermutations(n);``    ``return` `0;``}`

## Java

 `// Java implementation of the``// above approach``class` `GFG{` `// Function to find the factorial``// of a number``static` `int` `fact(``int` `a)``{``    ``int` `i, f = ``1``;` `    ``// Loop to find the factorial``    ``// of the given number``    ``for``(i = ``2``; i <= a; i++)``        ``f = f * i;``    ` `    ``return` `f;``}` `// Function to find the number``// of permutations possible``// for a given String``static` `int` `permute(``int` `n, ``int` `r)``{``    ``int` `ans = ``0``;``    ``ans = (fact(n) / fact(n - r));``    ``return` `ans;``}` `// Function to find the total``// number of combinations possible``static` `int` `findPermutations(``int` `n)``{``    ``int` `sum = ``0``, P;``    ``for``(``int` `r = ``1``; r <= n; r++)``    ``{``        ``P = permute(n, r);``        ``sum = sum + P;``    ``}``    ``return` `sum;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``String str = ``"xz"``;``    ``int` `result, n;``    ``n = str.length();` `    ``System.out.print(findPermutations(n));``}``}` `// This code is contributed by Amit Katiyar`

## Python3

 `# Python3 program to implement``# the above approach` `# Function to find the factorial``# of a number``def` `fact(a):` `    ``f ``=` `1` `    ``# Loop to find the factorial``    ``# of the given number``    ``for` `i ``in` `range``(``2``, a ``+` `1``):``        ``f ``=` `f ``*` `i` `    ``return` `f` `# Function to find the number``# of permutations possible``# for a given string``def` `permute(n, r):` `    ``ans ``=` `0``    ``ans ``=` `fact(n) ``/``/` `fact(n ``-` `r)` `    ``return` `ans` `# Function to find the total``# number of combinations possible``def` `findPermutations(n):` `    ``sum` `=` `0``    ``for` `r ``in` `range``(``1``, n ``+` `1``):``        ``P ``=` `permute(n, r)``        ``sum` `=` `sum` `+` `P` `    ``return` `sum` `# Driver Code``str` `=` `"xz"``n ``=` `len``(``str``)` `# Function call``print``(findPermutations(n))` `# This code is contributed by Shivam Singh`

## C#

 `// C# implementation of the``// above approach``using` `System;` `class` `GFG{` `// Function to find the factorial``// of a number``static` `int` `fact(``int` `a)``{``    ``int` `i, f = 1;` `    ``// Loop to find the factorial``    ``// of the given number``    ``for``(i = 2; i <= a; i++)``        ``f = f * i;``    ` `    ``return` `f;``}` `// Function to find the number``// of permutations possible``// for a given String``static` `int` `permute(``int` `n, ``int` `r)``{``    ``int` `ans = 0;``    ``ans = (fact(n) / fact(n - r));``    ``return` `ans;``}` `// Function to find the total``// number of combinations possible``static` `int` `findPermutations(``int` `n)``{``    ``int` `sum = 0, P;``    ``for``(``int` `r = 1; r <= n; r++)``    ``{``        ``P = permute(n, r);``        ``sum = sum + P;``    ``}``    ``return` `sum;``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``String str = ``"xz"``;``    ``int` `n;``    ``n = str.Length;` `    ``Console.Write(findPermutations(n));``}``}` `// This code is contributed by amal kumar choubey`

## Javascript

 ``
Output:
`4`

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