# Count number of strings (made of R, G and B) using given combination

We need to make a string of size n. Each character of the string is either ‘R’, ‘B’ or ‘G’. In the final string there needs to be at least r number of ‘R’, at least b number of ‘B’ and at least g number of ‘G’ (such that r + g + b <= n). We need to find number of such strings possible.**Examples:**

Input : n = 4, r = 1, b = 1, g = 1. Output: 36 No. of 'R' >= 1, No. of ‘G’ >= 1, No. of ‘B’ >= 1 and (No. of ‘R’) + (No. of ‘B’) + (No. of ‘G’) = n then following cases are possible: 1. RBGR and its 12 permutation 2. RBGB and its 12 permutation 3. RBGG and its 12 permutation Hence answer is 36.

Asked in : Directi

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend **live classes **with experts, please refer **DSA Live Classes for Working Professionals **and **Competitive Programming Live for Students**.

- As R, B and G have to be included atleast for given no. of times. Remaining values = n -(r + b + g).
- Make all combinations for the remaining values.
- Consider each element one by one for the remaining values and sum up all the permutations.
- Return total no. of permutations of all the combinations.

## C++

`// C++ program to count number of possible strings` `// with n characters.` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to calculate number of strings` `int` `possibleStrings( ` `int` `n, ` `int` `r, ` `int` `b, ` `int` `g)` `{` ` ` `// Store factorial of numbers up to n` ` ` `// for further computation` ` ` `int` `fact[n+1];` ` ` `fact[0] = 1;` ` ` `for` `(` `int` `i = 1; i <= n; i++)` ` ` `fact[i] = fact[i-1] * i;` ` ` `// Find the remaining values to be added` ` ` `int` `left = n - (r+g+b);` ` ` `int` `sum = 0;` ` ` `// Make all possible combinations` ` ` `// of R, B and G for the remaining value` ` ` `for` `(` `int` `i = 0; i <= left; i++)` ` ` `{` ` ` `for` `(` `int` `j = 0; j<= left-i; j++)` ` ` `{` ` ` `int` `k = left - (i+j);` ` ` `// Compute permutation of each combination` ` ` `// one by one and add them.` ` ` `sum = sum + fact[n] /` ` ` `(fact[i+r]*fact[j+b]*fact[k+g]);` ` ` `}` ` ` `}` ` ` `// Return total no. of strings/permutation` ` ` `return` `sum;` `}` `// Drivers code` `int` `main()` `{` ` ` `int` `n = 4, r = 2;` ` ` `int` `b = 0, g = 1;` ` ` `cout << possibleStrings(n, r, b, g);` ` ` `return` `0;` `}` |

## Java

`// Java program to count number of possible` `// strings with n characters.` `class` `GFG{` ` ` ` ` `//Function to calculate number of strings` ` ` `static` `int` `possibleStrings( ` `int` `n, ` `int` `r, ` `int` `b, ` `int` `g)` ` ` `{` ` ` `// Store factorial of numbers up to n` ` ` `// for further computation` ` ` `int` `fact[] = ` `new` `int` `[n+` `1` `];` ` ` `fact[` `0` `] = ` `1` `;` ` ` `for` `(` `int` `i = ` `1` `; i <= n; i++)` ` ` `fact[i] = fact[i-` `1` `] * i;` ` ` `// Find the remaining values to be added` ` ` `int` `left = n - (r+g+b);` ` ` `int` `sum = ` `0` `;` ` ` `// Make all possible combinations` ` ` `// of R, B and G for the remaining value` ` ` `for` `(` `int` `i = ` `0` `; i <= left; i++)` ` ` `{` ` ` `for` `(` `int` `j = ` `0` `; j<= left-i; j++)` ` ` `{` ` ` `int` `k = left - (i+j);` ` ` `// Compute permutation of each combination` ` ` `// one by one and add them.` ` ` `sum = sum + fact[n] /` ` ` `(fact[i+r]*fact[j+b]*fact[k+g]);` ` ` `}` ` ` `}` ` ` `// Return total no. of strings/permutation` ` ` `return` `sum;` ` ` `}` ` ` `//Drivers code` ` ` `public` `static` `void` `main(String []args)` ` ` `{` ` ` `int` `n = ` `4` `, r = ` `2` `;` ` ` `int` `b = ` `0` `, g = ` `1` `;` ` ` `System.out.println(possibleStrings(n, r, b, g));` ` ` `}` `}` |

## Python3

`# Python 3 program to count number of` `# possible strings with n characters.` `# Function to calculate number of strings` `def` `possibleStrings(n, r, b, g):` ` ` ` ` `# Store factorial of numbers up to n` ` ` `# for further computation` ` ` `fact ` `=` `[` `0` `for` `i ` `in` `range` `(n ` `+` `1` `)]` ` ` `fact[` `0` `] ` `=` `1` ` ` `for` `i ` `in` `range` `(` `1` `, n ` `+` `1` `, ` `1` `):` ` ` `fact[i] ` `=` `fact[i ` `-` `1` `] ` `*` `i` ` ` `# Find the remaining values to be added` ` ` `left ` `=` `n ` `-` `(r ` `+` `g ` `+` `b)` ` ` `sum` `=` `0` ` ` `# Make all possible combinations of` ` ` `# R, B and G for the remaining value` ` ` `for` `i ` `in` `range` `(` `0` `, left ` `+` `1` `, ` `1` `):` ` ` `for` `j ` `in` `range` `(` `0` `, left ` `-` `i ` `+` `1` `, ` `1` `):` ` ` `k ` `=` `left ` `-` `(i ` `+` `j)` ` ` `# Compute permutation of each` ` ` `# combination one by one and add them.` ` ` `sum` `=` `(` `sum` `+` `fact[n] ` `/` `(fact[i ` `+` `r] ` `*` ` ` `fact[j ` `+` `b] ` `*` `fact[k ` `+` `g]))` ` ` ` ` `# Return total no. of` ` ` `# strings/permutation` ` ` `return` `sum` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `n ` `=` `4` ` ` `r ` `=` `2` ` ` `b ` `=` `0` ` ` `g ` `=` `1` ` ` `print` `(` `int` `(possibleStrings(n, r, b, g)))` ` ` `# This code is contributed by` `# Sanjit_Prasad` |

## C#

`// C# program to count number of possible` `// strings with n characters.` `using` `System;` `class` `GFG` `{` ` ` `//Function to calculate number of strings` ` ` `static` `int` `possibleStrings( ` `int` `n, ` `int` `r,` ` ` `int` `b, ` `int` `g)` ` ` `{` ` ` `// Store factorial of numbers up to n` ` ` `// for further computation` ` ` `int` `[] fact = ` `new` `int` `[n + 1];` ` ` `fact[0] = 1;` ` ` ` ` `for` `(` `int` `i = 1; i <= n; i++)` ` ` `fact[i] = fact[i - 1] * i;` ` ` `// Find the remaining values to be added` ` ` `int` `left = n - (r + g + b);` ` ` `int` `sum = 0;` ` ` `// Make all possible combinations` ` ` `// of R, B and G for the remaining value` ` ` `for` `(` `int` `i = 0; i <= left; i++)` ` ` `{` ` ` `for` `(` `int` `j = 0; j <= left - i; j++)` ` ` `{` ` ` `int` `k = left - (i + j);` ` ` `// Compute permutation of each combination` ` ` `// one by one and add them.` ` ` `sum = sum + fact[n] / (fact[i + r] *` ` ` `fact[j + b] * fact[k + g]);` ` ` `}` ` ` `}` ` ` `// Return total no. of strings/permutation` ` ` `return` `sum;` ` ` `}` ` ` `//Drivers code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 4, r = 2;` ` ` `int` `b = 0, g = 1;` ` ` `Console.WriteLine(possibleStrings(n, r, b, g));` ` ` `}` `}` `// This Code is contributed by Code_Mech.` |

## PHP

`<?php` `// PHP program to count number` `// of possible strings with` `// n characters.` `// Function to calculate` `// number of strings` `function` `possibleStrings( ` `$n` `, ` `$r` `, ` `$b` `, ` `$g` `)` `{` ` ` ` ` `// Store factorial of` ` ` `// numbers up to n for` ` ` `// further computation` ` ` `$fact` `[0] = 1;` ` ` `for` `(` `$i` `= 1; ` `$i` `<= ` `$n` `; ` `$i` `++)` ` ` `$fact` `[` `$i` `] = ` `$fact` `[` `$i` `- 1] * ` `$i` `;` ` ` `// Find the remaining` ` ` `// values to be added` ` ` `$left` `= ` `$n` `- (` `$r` `+ ` `$g` `+ ` `$b` `);` ` ` `$sum` `= 0;` ` ` `// Make all possible combinations` ` ` `// of R, B and G for the remaining value` ` ` `for` `(` `$i` `= 0; ` `$i` `<= ` `$left` `; ` `$i` `++)` ` ` `{` ` ` `for` `(` `$j` `= 0; ` `$j` `<= ` `$left` `- ` `$i` `; ` `$j` `++)` ` ` `{` ` ` `$k` `= ` `$left` `- (` `$i` `+` `$j` `);` ` ` `// Compute permutation of` ` ` `// each combination one` ` ` `// by one and add them.` ` ` `$sum` `= ` `$sum` `+ ` `$fact` `[` `$n` `] /` ` ` `(` `$fact` `[` `$i` `+ ` `$r` `] *` ` ` `$fact` `[` `$j` `+ ` `$b` `] *` ` ` `$fact` `[` `$k` `+ ` `$g` `]);` ` ` `}` ` ` `}` ` ` `// Return total no. of` ` ` `// strings/permutation` ` ` `return` `$sum` `;` `}` ` ` `// Driver Code` ` ` `$n` `= 4; ` `$r` `= 2;` ` ` `$b` `= 0; ` `$g` `= 1;` ` ` ` ` `echo` `possibleStrings(` `$n` `, ` `$r` `, ` `$b` `, ` `$g` `);` `// This code is contributed by jit_t.` `?>` |

## Javascript

`<script>` `// Javascript program to count number of possible` `// strings with n characters.` ` ` ` ` `// Function to calculate number of strings` ` ` `function` `possibleStrings(n,r,b,g)` ` ` `{` ` ` `// Store factorial of numbers up to n` ` ` `// for further computation` ` ` `let fact = ` `new` `Array(n+1);` ` ` `fact[0] = 1;` ` ` `for` `(let i = 1; i <= n; i++)` ` ` `fact[i] = fact[i-1] * i;` ` ` ` ` `// Find the remaining values to be added` ` ` `let left = n - (r+g+b);` ` ` `let sum = 0;` ` ` ` ` `// Make all possible combinations` ` ` `// of R, B and G for the remaining value` ` ` `for` `(let i = 0; i <= left; i++)` ` ` `{` ` ` `for` `(let j = 0; j<= left-i; j++)` ` ` `{` ` ` `let k = left - (i+j);` ` ` ` ` `// Compute permutation of each combination` ` ` `// one by one and add them.` ` ` `sum = sum + fact[n] /` ` ` `(fact[i+r]*fact[j+b]*fact[k+g]);` ` ` `}` ` ` `}` ` ` ` ` `// Return total no. of strings/permutation` ` ` `return` `sum;` ` ` `}` ` ` ` ` `// Drivers code` ` ` `let n = 4, r = 2;` ` ` `let b = 0, g = 1;` ` ` `document.write(possibleStrings(n, r, b, g));` ` ` ` ` `// This code is contributed by avanitrachhadiya2155` ` ` `</script>` |

**Output:**

22

To handle n with large numbers, we can use the concept of Large Factorial.

This article is contributed by **Sahil Chhabra**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.