# Count of N size strings consisting of at least one vowel and one consonant

Last Updated : 08 Mar, 2022

Given an integer N, which represents the length of a string, the task is to count the number of strings possible of length N which consists of only one vowel and one consonant.
Note: Since the output can be large print in modulo 1000000007
Examples:

Input: N = 2
Output: 210
Explanation:
There are 5 vowels and 21 consonants in English alphabets.
So for vowel ‘a’ we can have 42 strings of the form ‘ab’, ‘ba’, ‘ac’, ‘ca’, ‘ad’, ‘da’ and so on.
For the other 4 vowels, the same process repeats, and we get a total of 210 such strings.
Input: N = 3
Output: 8190

Approach:
To solve the problem mentioned above, we need to ignore the strings that comprise only vowels(to allow at least one consonant) and only consonants(to allow at least one vowel). Hence, the required answer is:

All N length strings possible – (N length strings consisting of only vowels + N length strings consisting of only consonants) = 26 N – (5 N + 21 N

Below is the implementation of the above approach:

## C++

 `// C++ program to count all` `// possible strings of length N` `// consisting of atleast one` `// vowel and one consonant` `#include ` `using` `namespace` `std;`   `const` `unsigned ``long` `long` `mod = 1e9 + 7;`   `// Function to return base^exponent` `unsigned ``long` `long` `expo(` `    ``unsigned ``long` `long` `base,` `    ``unsigned ``long` `long` `exponent)` `{`   `    ``unsigned ``long` `long` `ans = 1;`   `    ``while` `(exponent != 0) {` `        ``if` `((exponent & 1) == 1) {` `            ``ans = ans * base;` `            ``ans = ans % mod;` `        ``}`   `        ``base = base * base;` `        ``base %= mod;` `        ``exponent >>= 1;` `    ``}`   `    ``return` `ans % mod;` `}`   `// Function to count all possible strings` `unsigned ``long` `long` `findCount(` `    ``unsigned ``long` `long` `N)` `{` `    ``// All possible strings of length N` `    ``unsigned ``long` `long` `ans` `        ``= (expo(26, N)`   `           ``// vowels only` `           ``- expo(5, N)`   `           ``// consonants only` `           ``- expo(21, N))`   `          ``% mod;`   `    ``ans += mod;` `    ``ans %= mod;`   `    ``// Return the` `    ``// final result` `    ``return` `ans;` `}`   `// Driver Program` `int` `main()` `{` `    ``unsigned ``long` `long` `N = 3;` `    ``cout << findCount(N);`   `    ``return` `0;` `}`

## Java

 `// Java program to count all` `// possible Strings of length N` `// consisting of atleast one` `// vowel and one consonant` `class` `GFG{`   `static` `int` `mod = (``int``) (1e9 + ``7``);`   `// Function to return base^exponent` `static` `int` `expo(``int` `base, ``int` `exponent)` `{` `    ``int` `ans = ``1``;`   `    ``while` `(exponent != ``0``)` `    ``{` `        ``if` `((exponent & ``1``) == ``1``)` `        ``{` `            ``ans = ans * base;` `            ``ans = ans % mod;` `        ``}` `        ``base = base * base;` `        ``base %= mod;` `        ``exponent >>= ``1``;` `    ``}` `    ``return` `ans % mod;` `}`   `// Function to count all possible Strings` `static` `int` `findCount(``int` `N)` `{` `    `  `    ``// All possible Strings of length N` `    ``int` `ans = (expo(``26``, N) - ` `              `  `               ``// Vowels only` `               ``expo(``5``, N) - ` `               `  `               ``// Consonants only` `               ``expo(``21``, N))% mod;` `    ``ans += mod;` `    ``ans %= mod;`   `    ``// Return the` `    ``// final result` `    ``return` `ans;` `}`   `// Driver code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `N = ``3``;` `    ``System.out.print(findCount(N));` `}` `}`   `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 program to count all` `# possible strings of length N` `# consisting of atleast one` `# vowel and one consonant` `mod ``=` `1e9` `+` `7`   `# Function to return base^exponent` `def` `expo(base, exponent):` `    ``ans ``=` `1` `    ``while` `(exponent !``=` `0``):` `        ``if` `((exponent & ``1``) ``=``=` `1``):` `            ``ans ``=` `ans ``*` `base` `            ``ans ``=` `ans ``%` `mod`   `        ``base ``=` `base ``*` `base` `        ``base ``%``=` `mod` `        ``exponent >>``=` `1`   `    ``return` `ans ``%` `mod`   `# Function to count all ` `# possible strings` `def` `findCount(N):`   `    ``# All possible strings ` `    ``# of length N` `    ``ans ``=` `((expo(``26``, N) ``-` `            `  `            ``# vowels only` `            ``expo(``5``, N) ``-`   `            ``# consonants only` `            ``expo(``21``, N)) ``%` `            ``mod)`   `    ``ans ``+``=` `mod` `    ``ans ``%``=` `mod`   `    ``# Return the` `    ``# final result` `    ``return` `ans`   `# Driver Program` `if` `__name__ ``=``=` `"__main__"``:` `    ``N ``=` `3` `    ``print` `(``int``(findCount(N)))`   `# This code is contributed by Chitranayal`

## C#

 `// C# program to count all possible Strings` `// of length N consisting of atleast one` `// vowel and one consonant` `using` `System;`   `class` `GFG{`   `static` `int` `mod = (``int``)(1e9 + 7);`   `// Function to return base^exponent` `static` `int` `expo(``int` `Base, ``int` `exponent)` `{` `    ``int` `ans = 1;`   `    ``while` `(exponent != 0)` `    ``{` `        ``if` `((exponent & 1) == 1)` `        ``{` `            ``ans = ans * Base;` `            ``ans = ans % mod;` `        ``}` `        ``Base = Base * Base;` `        ``Base %= mod;` `        ``exponent >>= 1;` `    ``}` `    ``return` `ans % mod;` `}`   `// Function to count all possible Strings` `static` `int` `findCount(``int` `N)` `{` `    `  `    ``// All possible Strings of length N` `    ``int` `ans = (expo(26, N) - ` `               `  `               ``// Vowels only` `               ``expo(5, N) - ` `               `  `               ``// Consonants only` `               ``expo(21, N)) % mod;` `    ``ans += mod;` `    ``ans %= mod;`   `    ``// Return the` `    ``// readonly result` `    ``return` `ans;` `}`   `// Driver code` `public` `static` `void` `Main(String[] args)` `{` `    ``int` `N = 3;` `    `  `    ``Console.Write(findCount(N));` `}` `}`   `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output

`8190`

Time Complexity: O(log10N)

Auxiliary Space: O(1)