Related Articles
Permutations of n things taken r at a time with k things together
• Difficulty Level : Basic
• Last Updated : 08 Mar, 2021

Given n, r and K. The task is to find the number of permutations of different things taken at a time such that specific things always occur together.
Examples:

Input : n = 8, r = 5, k = 2
Output : 960

Input : n = 6, r = 2, k = 2
Output : 2

Approach:

1. A bundle of specific things can be put in r places in (r – k + 1) ways .
2. k specific things in the bundle can be arranged themselves into k! ways.
3. Now (n – k) things will be arranged in (r – k) places in ways.

Thus, using the fundamental principle of counting, the required number of permutations will be:

Below is the implementation of the above approach:

C++

 // CPP program to find the number of permutations of// n different things taken r at a time// with k things grouped together #include using namespace std; // Function to find factorial// of a numberint factorial(int n){    int fact = 1;     for (int i = 2; i <= n; i++)        fact = fact * i;     return fact;} // Function to calculate p(n, r)int npr(int n, int r){    int pnr = factorial(n) / factorial(n - r);     return pnr;} // Function to find the number of permutations of// n different things taken r at a time// with k things grouped togetherint countPermutations(int n, int r, int k){    return factorial(k) * (r - k + 1) * npr(n - k, r - k);} // Driver codeint main(){    int n = 8;    int r = 5;    int k = 2;     cout << countPermutations(n, r, k);     return 0;}

Java

 // Java program to find the number of permutations of// n different things taken r at a time// with k things grouped together class GFG{// Function to find factorial// of a numberstatic int factorial(int n){    int fact = 1;     for (int i = 2; i <= n; i++)        fact = fact * i;     return fact;} // Function to calculate p(n, r)static int npr(int n, int r){    int pnr = factorial(n) / factorial(n - r);     return pnr;} // Function to find the number of permutations of// n different things taken r at a time// with k things grouped togetherstatic int countPermutations(int n, int r, int k){    return factorial(k) * (r - k + 1) * npr(n - k, r - k);} // Driver codepublic static void main(String[] args){    int n = 8;    int r = 5;    int k = 2;     System.out.println(countPermutations(n, r, k));}}// this code is contributed by mits

Python3

 # Python3 program to find the number of permutations of# n different things taken r at a time# with k things grouped together # def to find factorial# of a numberdef factorial(n):      fact = 1;     for i in range(2,n+1):        fact = fact * i;     return fact;   # def to calculate p(n, r)def npr(n, r):      pnr = factorial(n) / factorial(n - r);     return pnr;   # def to find the number of permutations of# n different things taken r at a time# with k things grouped togetherdef countPermutations(n, r, k):      return int(factorial(k) * (r - k + 1) * npr(n - k, r - k));   # Driver coden = 8;r = 5;k = 2; print(countPermutations(n, r, k));     # this code is contributed by mits

C#

 // C# program to find the number of// permutations of n different things// taken r at a time with k things// grouped togetherusing System; class GFG{     // Function to find factorial// of a numberstatic int factorial(int n){    int fact = 1;     for (int i = 2; i <= n; i++)        fact = fact * i;     return fact;} // Function to calculate p(n, r)static int npr(int n, int r){    int pnr = factorial(n) /              factorial(n - r);     return pnr;} // Function to find the number of// permutations of n different// things taken r at a time with// k things grouped togetherstatic int countPermutations(int n,                             int r, int k){    return factorial(k) * (r - k + 1) *                    npr(n - k, r - k);} // Driver codestatic void Main(){    int n = 8;    int r = 5;    int k = 2;     Console.WriteLine(countPermutations(n, r, k));}} // This code is contributed by mits

PHP

 

Javascript

 
Output:
960

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 industry experts, please refer Geeks Classes Live

My Personal Notes arrow_drop_up