Sum of all products of the Binomial Coefficients of two numbers up to K | Java implementation of the above approach ; Function returns nCr i . e . Binomial Coefficient ; Initialize res with 1 ; Since C ( n , r ) = C ( n , n - r ) ; Evaluating expression ; Function to calculate and return the sum of the products ; Initialize sum to 0 ; Traverse from 0 to k ; Driver Code
import java . util . * ; class GFG { static int nCr ( int n , int r ) { int res = 1 ; if ( r > n - r ) r = n - r ; for ( int i = 0 ; i < r ; ++ i ) { res *= ( n - i ) ; res /= ( i + 1 ) ; } return res ; } static int solve ( int n , int m , int k ) { int sum = 0 ; for ( int i = 0 ; i <= k ; i ++ ) sum += nCr ( n , i ) * nCr ( m , k - i ) ; return sum ; } public static void main ( String [ ] args ) { int n = 3 , m = 2 , k = 2 ; System . out . print ( solve ( n , m , k ) ) ; } }