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C++ Permutations of n things Taken r at a Time with k Things Together
Given n, r, k, now we have to find how we can select r things from n so that specific k things always occur together, for example.
Input : n = 8, r = 5, k = 2 Output : 960 Input : n = 6, r = 2, k = 2 Output : 2
We need a little knowledge for this problem because this problem is asking us to find the permutation of n and r such that k things come together.
Approach to Find the Solution
We need to formulate our formula for this question, and that will give us our answer.
Example
#include <bits/stdc++.h>
using namespace std;
int fact(int n){ // function to calculate factorial of a number
if(n <= 1)
return 1;
return n * fact(n-1);
}
int npr(int n, int r){ // finding permutation
int pnr = fact(n) / fact(n - r);
return pnr;
}
int countPermutations(int n, int r, int k){ // the formula that we came up with
return fact(k) * (r - k + 1) * npr(n - k, r - k);
}
int main(){
int n = 8;
int r = 5;
int k = 2;
cout << countPermutations(n, r, k);
return 0;
}Output
960
Explanation of the Above Code
In the above approach, we try to devise our formula for calculating our answer as for this problem, the formula that we devised is (k!) * (r - k + 1) * P(n-k, r-k). ( P(x, y) is the number of permutations of selection y from x) hence we put up our formula, and we calculate the answer.
Conclusion
In this tutorial, we solve a problem to find Permutations of n things taken r at a time with k things together. We also learned the C++ program for this problem and the complete approach ( Normal) by which we solved this problem.
We can write the same program in other languages such as C, java, python, and other languages. We hope you find this tutorial helpful.
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