# 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

- 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 permuations.
- 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; ` `} ` |

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## 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)); ` ` ` `} ` `} ` |

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## 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 ` |

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## 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. ` |

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## 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. ` `?> ` |

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**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 contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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