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The binomial coefficient is a quotation found in a binary theorem which can be arranged in a form of pascal triangle it is a combination of numbers which is equal to nCr where r is selected from a set of n items which shows the following formula

nCr=n! / r!(n-r)! or nCr=n(n-1)(n-2).....(n-r+1) / r!

The sum of the square of Binomial Coefficient i.e
(_{n}C_{0})^{2} + (_{n}C_{1})^{2} + (_{n}C_{2})^{2} + (_{n}C_{3})^{2} + ……… + (_{n}C_{n-2})^{2} + (_{n}C_{n-1})^{2} + (_{n}C_{n})^{2}

Input :n=5 Output:252

In this program first we have to find the binomial coefficient of r which is selected from n set then we have to square each coefficient and sum them we can derive a formula from the above equation or use of factorial function of each digit to get a sum so we will fall or factorial function in which we will pass and r for a given equation and then add it then we get the solution

#include <iostream> using namespace std; int fact(int n){ int fact = 1, i; for (i = 2; i <= n; i++){ fact *= i; } return fact; } int main(){ int n=5; int sum = 0; int temp=0; for (int r = 0; r <= n; r++){ temp = fact(n)/(fact(r)*fact(n-r)); sum +=(temp*temp); } cout<<sum; return 0; }

252

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