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Number of words that can be made using exactly P consonants and Q vowels from the given string

• Difficulty Level : Medium
• Last Updated : 01 Apr, 2021

Given a string str and two integers P and Q. The task is to find the total count of words that can be formed by choosing exactly P consonants and Q vowels from the given string.
Examples:

Input: str = “geek”, P = 1, Q = 1
Output:
“ge”, “ge”, “eg”, “ek”, “eg”, “ek”,
“ke” and “ke” are the possible words.
Input: str = “crackathon”, P = 4, Q = 3
Output: 176400

Approach: Since P consonants and Q vowels has to be chosen from the original count of consonants and vowels in the given string. So, binomial coefficient can be used to calculate the combinations of choosing these characters and the characters chosen can be arranged in themselves using the factorial of their count.
Below is the implementation of the above approach:

C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `#define lli long long int` `// Function to return the value of nCk``lli binomialCoeff(lli n, lli k)``{``    ``if` `(k == 0 || k == n)``        ``return` `1;` `    ``return` `binomialCoeff(n - 1, k - 1)``           ``+ binomialCoeff(n - 1, k);``}` `// Function to return the factorial of n``lli fact(lli n)``{``    ``if` `(n >= 1)``        ``return` `n * fact(n - 1);``    ``else``        ``return` `1;``}` `// Function that returns true if ch is a vowel``bool` `isVowel(``char` `ch)``{``    ``if` `(ch == ``'a'` `|| ch == ``'e'` `|| ch == ``'i'``        ``|| ch == ``'o'` `|| ch == ``'u'``) {``        ``return` `true``;``    ``}` `    ``return` `false``;``}` `// Function to return the number of words possible``lli countWords(string s, ``int` `p, ``int` `q)``{` `    ``// To store the count of vowels and``    ``// consonanats in the given string``    ``lli countc = 0, countv = 0;``    ``for` `(``int` `i = 0; i < s.length(); i++) {` `        ``// If current character is a vowel``        ``if` `(isVowel(s[i]))``            ``countv++;``        ``else``            ``countc++;``    ``}` `    ``// Find the total possible words``    ``lli a = binomialCoeff(countc, p);``    ``lli b = binomialCoeff(countv, q);``    ``lli c = fact(p + q);``    ``lli ans = (a * b) * c;``    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``string s = ``"crackathon"``;``    ``int` `p = 4, q = 3;` `    ``cout << countWords(s, p, q);` `    ``return` `0;``}`

Java

 `// Java implementation of the above approach``class` `GFG``{``    ` `    ``// Function to return the value of nCk``    ``static` `long` `binomialCoeff(``long` `n, ``long` `k)``    ``{``        ``if` `(k == ``0` `|| k == n)``            ``return` `1``;``    ` `        ``return` `binomialCoeff(n - ``1``, k - ``1``) +``               ``binomialCoeff(n - ``1``, k);``    ``}``    ` `    ``// Function to return the factorial of n``    ``static` `long` `fact(``long` `n)``    ``{``        ``if` `(n >= ``1``)``            ``return` `n * fact(n - ``1``);``        ``else``            ``return` `1``;``    ``}``    ` `    ``// Function that returns true if ch is a vowel``    ``static` `boolean` `isVowel(``char` `ch)``    ``{``        ``if` `(ch == ``'a'` `|| ch == ``'e'` `|| ch == ``'i'` `||``                         ``ch == ``'o'` `|| ch == ``'u'``)``        ``{``            ``return` `true``;``        ``}``    ` `        ``return` `false``;``    ``}``    ` `    ``// Function to return the number of words possible``    ``static` `long` `countWords(String s, ``int` `p, ``int` `q)``    ``{``    ` `        ``// To store the count of vowels and``        ``// consonanats in the given string``        ``long` `countc = ``0``, countv = ``0``;``        ``for` `(``int` `i = ``0``; i < s.length(); i++)``        ``{``    ` `            ``// If current character is a vowel``            ``if` `(isVowel(s.charAt(i)))``                ``countv++;``            ``else``                ``countc++;``        ``}``    ` `        ``// Find the total possible words``        ``long` `a = binomialCoeff(countc, p);``        ``long` `b = binomialCoeff(countv, q);``        ``long` `c = fact(p + q);``        ``long` `ans = (a * b) * c;``        ``return` `ans;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``String s = ``"crackathon"``;``        ``int` `p = ``4``, q = ``3``;``    ` `        ``System.out.println(countWords(s, p, q));``    ``}``}` `// This Code is contributed by AnkitRai01`

Python3

 `# Python3 implementation of the approach` `# Function to return the value of nCk``def` `binomialCoeff(n, k):``    ``if` `(k ``=``=` `0` `or` `k ``=``=` `n):``        ``return` `1` `    ``return` `binomialCoeff(n ``-` `1``, k ``-` `1``) ``+` `\``           ``binomialCoeff(n ``-` `1``, k)` `# Function to return the factorial of n``def` `fact(n):``    ``if` `(n >``=` `1``):``        ``return` `n ``*` `fact(n ``-` `1``)``    ``else``:``        ``return` `1` `# Function that returns true if ch is a vowel``def` `isVowel(ch):` `    ``if` `(ch ``=``=` `'a'` `or` `ch ``=``=` `'e'` `or``        ``ch ``=``=` `'i'` `or` `ch ``=``=` `'o'` `or` `ch ``=``=` `'u'``):``        ``return` `True` `    ``return` `False` `# Function to return the number of words possible``def` `countWords(s, p, q):` `    ``# To store the count of vowels and``    ``# consonanats in the given string``    ``countc ``=` `0``    ``countv ``=` `0``    ``for` `i ``in` `range``(``len``(s)):` `        ``# If current character is a vowel``        ``if` `(isVowel(s[i])):``            ``countv ``+``=` `1``        ``else``:``            ``countc ``+``=` `1` `    ``# Find the total possible words``    ``a ``=` `binomialCoeff(countc, p)``    ``b ``=` `binomialCoeff(countv, q)``    ``c ``=` `fact(p ``+` `q)``    ``ans ``=` `(a ``*` `b) ``*` `c``    ``return` `ans` `# Driver code``s ``=` `"crackathon"``p ``=` `4``q ``=` `3` `print``(countWords(s, p, q))` `# This code is contributed by Mohit Kumar`

C#

 `// C# implementation of the approach``using` `System;``using` `System.Collections.Generic;``    ` `class` `GFG``{``    ` `    ``// Function to return the value of nCk``    ``static` `long` `binomialCoeff(``long` `n, ``long` `k)``    ``{``        ``if` `(k == 0 || k == n)``            ``return` `1;``    ` `        ``return` `binomialCoeff(n - 1, k - 1) +``               ``binomialCoeff(n - 1, k);``    ``}``    ` `    ``// Function to return the factorial of n``    ``static` `long` `fact(``long` `n)``    ``{``        ``if` `(n >= 1)``            ``return` `n * fact(n - 1);``        ``else``            ``return` `1;``    ``}``    ` `    ``// Function that returns true if ch is a vowel``    ``static` `bool` `isVowel(``char` `ch)``    ``{``        ``if` `(ch == ``'a'` `|| ch == ``'e'` `|| ch == ``'i'` `||``                         ``ch == ``'o'` `|| ch == ``'u'``)``        ``{``            ``return` `true``;``        ``}``        ``return` `false``;``    ``}``    ` `    ``// Function to return the number of words possible``    ``static` `long` `countWords(String s, ``int` `p, ``int` `q)``    ``{``    ` `        ``// To store the count of vowels and``        ``// consonanats in the given string``        ``long` `countc = 0, countv = 0;``        ``for` `(``int` `i = 0; i < s.Length; i++)``        ``{``    ` `            ``// If current character is a vowel``            ``if` `(isVowel(s[i]))``                ``countv++;``            ``else``                ``countc++;``        ``}``    ` `        ``// Find the total possible words``        ``long` `a = binomialCoeff(countc, p);``        ``long` `b = binomialCoeff(countv, q);``        ``long` `c = fact(p + q);``        ``long` `ans = (a * b) * c;``        ``return` `ans;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main (String[] args)``    ``{``        ``String s = ``"crackathon"``;``        ``int` `p = 4, q = 3;``    ` `        ``Console.WriteLine(countWords(s, p, q));``    ``}``}` `// This code is contributed by PrinciRaj1992`

Javascript

 ``
Output:
`176400`

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