# Number of ways to arrange a word such that all vowels occur together

• Difficulty Level : Medium
• Last Updated : 06 May, 2021

Given a word containing vowels and consonants. The task is to find that in how many ways to word can be arranged so that the vowels always come together. Given that the length of the word <10.

Examples:

```Input: str = "geek"
Output: 6
Ways such that both 'e' comes together are 6
i.e. geek, gkee, kgee, eekg, eegk, keeg

Input: str = "corporation"
Output: 50400```

Approach: Since word contains vowels and consonants together. All vowels are needed to remain together then we will take all vowels as a single letter.

As, in the word ‘geeksforgeeks’, we can treat the vowels “eeoee” as one letter.
Thus, we have gksfrgks (eeoee)
This has 9 (8 + 1) letters of which g, k, s each occurs 2 times and the rest are different.
The number of ways arranging these letters = 9!/(2!)x(2!)x(2!) = 45360 ways
Now, 5 vowels in which ‘e’ occurs 4 times and ‘o’ occurs 1 time, can be arranged in 5! /4! = 5 ways.
Required number of ways = (45360 x 5) = 226800

Below is the implementation of the above approach:

## C++

 `// C++ program to calculate the no. of ways``// to arrange the word having vowels together``#include ``#define ll long long int``using` `namespace` `std;` `// Factorial of a number``ll fact(``int` `n)``{``    ``ll f = 1;``    ``for` `(``int` `i = 2; i <= n; i++)``        ``f = f * i;``    ``return` `f;``}` `// calculating ways for arranging consonants``ll waysOfConsonants(``int` `size1, ``int` `freq[])``{``    ``ll ans = fact(size1);``    ``for` `(``int` `i = 0; i < 26; i++) {` `        ``// Ignore vowels``        ``if` `(i == 0 || i == 4 || i == 8 || i == 14 || i == 20)``            ``continue``;``        ``else``            ``ans = ans / fact(freq[i]);``    ``}` `    ``return` `ans;``}` `// calculating ways for arranging vowels``ll waysOfVowels(``int` `size2, ``int` `freq[])``{``    ``return` `fact(size2) / (fact(freq[0]) * fact(freq[4]) * fact(freq[8])``                    ``* fact(freq[14]) * fact(freq[20]));``}` `// Function to count total no. of ways``ll countWays(string str)``{` `    ``int` `freq[26] = { 0 };``    ``for` `(``int` `i = 0; i < str.length(); i++)``        ``freq[str[i] - ``'a'``]++;` `    ``// Count vowels and consonant``    ``int` `vowel = 0, consonant = 0;``    ``for` `(``int` `i = 0; i < str.length(); i++) {` `        ``if` `(str[i] != ``'a'` `&& str[i] != ``'e'` `&& str[i] != ``'i'``            ``&& str[i] != ``'o'` `&& str[i] != ``'u'``)``            ``consonant++;``        ``else``            ``vowel++;``    ``}` `    ``// total no. of ways``    ``return` `waysOfConsonants(consonant+1, freq) *``           ``waysOfVowels(vowel, freq);``}` `// Driver code``int` `main()``{``    ``string str = ``"geeksforgeeks"``;` `    ``cout << countWays(str) << endl;` `    ``return` `0;``}`

## Java

 `// Java program to calculate the no. of``// ways to arrange the word having``// vowels together``import` `java.util.*;`` ` `class` `GFG{`` ` `// Factorial of a number``static` `int` `fact(``int` `n)``{``    ``int` `f = ``1``;``    ``for``(``int` `i = ``2``; i <= n; i++)``        ``f = f * i;``         ` `    ``return` `f;``}`` ` `// Calculating ways for arranging consonants``static` `int` `waysOfConsonants(``int` `size1,``                            ``int` `[]freq)``{``    ``int` `ans = fact(size1);``    ``for``(``int` `i = ``0``; i < ``26``; i++)``    ``{``         ` `        ``// Ignore vowels``        ``if` `(i == ``0` `|| i == ``4` `|| i == ``8` `||``            ``i == ``14` `|| i == ``20``)``            ``continue``;``        ``else``            ``ans = ans / fact(freq[i]);``    ``}``    ``return` `ans;``}`` ` `// Calculating ways for arranging vowels``static` `int` `waysOfVowels(``int` `size2, ``int` `[] freq)``{``    ``return` `fact(size2) / (fact(freq[``0``]) *``          ``fact(freq[``4``]) * fact(freq[``8``]) *``         ``fact(freq[``14``]) * fact(freq[``20``]));``}`` ` `// Function to count total no. of ways``static` `int` `countWays(String str)``{``    ``int` `[]freq = ``new` `int` `[``200``];``    ``for``(``int` `i = ``0``; i < ``200``; i++)``        ``freq[i] = ``0``;``         ` `    ``for``(``int` `i = ``0``; i < str.length(); i++)``        ``freq[str.charAt(i) - ``'a'``]++;``         ` `    ``// Count vowels and consonant``    ``int` `vowel = ``0``, consonant = ``0``;``    ``for``(``int` `i = ``0``; i < str.length(); i++)``    ``{``        ``if` `(str.charAt(i) != ``'a'` `&& str.charAt(i) != ``'e'` `&&``            ``str.charAt(i) != ``'i'` `&& str.charAt(i) != ``'o'` `&&``            ``str.charAt(i) != ``'u'``)``            ``consonant++;``        ``else``            ``vowel++;``    ``}`` ` `    ``// Total no. of ways``    ``return` `waysOfConsonants(consonant + ``1``, freq) *``           ``waysOfVowels(vowel, freq);``}`` ` `// Driver code``public` `static` `void` `main(String []args)``{``    ``String str = ``"geeksforgeeks"``;`` ` `    ``System.out.println(countWays(str));``}``}` `// This code is contributed by rutvik_56`

## Python3

 `# Python3 program to calculate``# the no. of ways to arrange``# the word having vowels together` `# Factorial of a number``def` `fact(n):` `    ``f ``=` `1``    ``for` `i ``in` `range``(``2``, n ``+` `1``):``        ``f ``=` `f ``*` `i``    ``return` `f` `# calculating ways for``# arranging consonants``def` `waysOfConsonants(size1, freq):` `    ``ans ``=` `fact(size1)``    ``for` `i ``in` `range``(``26``):` `        ``# Ignore vowels``        ``if` `(i ``=``=` `0` `or` `i ``=``=` `4` `or``            ``i ``=``=` `8` `or` `i ``=``=` `14` `or``            ``i ``=``=` `20``):``            ``continue``        ``else``:``            ``ans ``=` `ans ``/``/` `fact(freq[i])` `    ``return` `ans` `# calculating ways for``# arranging vowels``def` `waysOfVowels(size2, freq):` `    ``return` `(fact(size2) ``/``/` `(fact(freq[``0``]) ``*``            ``fact(freq[``4``]) ``*` `fact(freq[``8``]) ``*``            ``fact(freq[``14``]) ``*` `fact(freq[``20``])))` `# Function to count total no. of ways``def` `countWays(str1):` `    ``freq ``=` `[``0``] ``*` `26``    ``for` `i ``in` `range``(``len``(str1)):``        ``freq[``ord``(str1[i]) ``-``             ``ord``(``'a'``)] ``+``=` `1` `    ``# Count vowels and consonant``    ``vowel ``=` `0``    ``consonant ``=` `0``    ``for` `i ``in` `range``(``len``(str1)):` `        ``if` `(str1[i] !``=` `'a'` `and` `str1[i] !``=` `'e'` `and``            ``str1[i] !``=` `'i'` `and` `str1[i] !``=` `'o'` `and``            ``str1[i] !``=` `'u'``):``            ``consonant ``+``=` `1``        ``else``:``            ``vowel ``+``=` `1` `    ``# total no. of ways``    ``return` `(waysOfConsonants(consonant ``+` `1``, freq) ``*``            ``waysOfVowels(vowel, freq))` `# Driver code``if` `__name__ ``=``=` `"__main__"``:` `    ``str1 ``=` `"geeksforgeeks"``    ``print``(countWays(str1))` `# This code is contributed by Chitranayal`

## C#

 `// C# program to calculate the no. of``// ways to arrange the word having``// vowels together``using` `System.Collections.Generic;``using` `System;` `class` `GFG{` `// Factorial of a number``static` `int` `fact(``int` `n)``{``    ``int` `f = 1;``    ``for``(``int` `i = 2; i <= n; i++)``        ``f = f * i;``        ` `    ``return` `f;``}` `// Calculating ways for arranging consonants``static` `int` `waysOfConsonants(``int` `size1,``                            ``int` `[]freq)``{``    ``int` `ans = fact(size1);``    ``for``(``int` `i = 0; i < 26; i++)``    ``{``        ` `        ``// Ignore vowels``        ``if` `(i == 0 || i == 4 || i == 8 ||``            ``i == 14 || i == 20)``            ``continue``;``        ``else``            ``ans = ans / fact(freq[i]);``    ``}``    ``return` `ans;``}` `// Calculating ways for arranging vowels``static` `int` `waysOfVowels(``int` `size2, ``int` `[] freq)``{``    ``return` `fact(size2) / (fact(freq[0]) *``          ``fact(freq[4]) * fact(freq[8]) *``         ``fact(freq[14]) * fact(freq[20]));``}` `// Function to count total no. of ways``static` `int` `countWays(``string` `str)``{``    ``int` `[]freq = ``new` `int` `[200];``    ``for``(``int` `i = 0; i < 200; i++)``        ``freq[i] = 0;``        ` `    ``for``(``int` `i = 0; i < str.Length; i++)``        ``freq[str[i] - ``'a'``]++;``        ` `    ``// Count vowels and consonant``    ``int` `vowel = 0, consonant = 0;``    ``for``(``int` `i = 0; i < str.Length; i++)``    ``{``        ``if` `(str[i] != ``'a'` `&& str[i] != ``'e'` `&&``            ``str[i] != ``'i'` `&& str[i] != ``'o'` `&&``            ``str[i] != ``'u'``)``            ``consonant++;``        ``else``            ``vowel++;``    ``}` `    ``// Total no. of ways``    ``return` `waysOfConsonants(consonant + 1, freq) *``           ``waysOfVowels(vowel, freq);``}` `// Driver code``public` `static` `void` `Main()``{``    ``string` `str = ``"geeksforgeeks"``;` `    ``Console.WriteLine(countWays(str));``}``}` `// This code is contributed by Stream_Cipher`

## Javascript

 ``

Output:

`226800`

Further Optimizations: We can pre-compute required factorial values to avoid re-computations.

My Personal Notes arrow_drop_up