Write a function called committee to compute the number of ways of forming a single committee with r members from a collection of n people. This is the same as computing the number of ways of choosing r people out of n to sit at the first of two tables, and is therefore n! / (r!*(n-r)!). Make sure the function returns an integer, not a floating point number with a decimal point.

This program is written in C++.  The explanation of the code is given below in the explanation section.

Explanation:

#include <iostream>

using namespace std;

//factorial calculation

int fact(int n) {

  if (n == 0 || n == 1)

     return 1;

  else

     return n * fact(n - 1);

}

int main() {

  int n, r, comb; /* n represent number of people (population), r represent the number of selection from population and combination represent number of ways or combination */

  cout<<"Enter n : ";// prompt user to enter population i.e. total number of people

  cin>>n;//store into n

  cout<<"\nEnter r : ";//prompt user to enter number of selection from population

  cin>>r;

  comb = fact(n) / (fact(r) * fact(n-r));// calcuate combination- number of differnt ways to form a committe

  cout << "\nCombination : " << comb; //show the result

  return 0;

}

solution:

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