function value = i4_choose ( n, k ) %*****************************************************************************80 % %% I4_CHOOSE computes the binomial coefficient C(N,K) as an I4. % % Discussion: % % The value is calculated in such a way as to avoid overflow and % roundoff. The calculation is done in integer arithmetic. % % The formula used is: % % C(N,K) = N! / ( K! * (N-K)! ) % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 30 October 2014 % % Author: % % John Burkardt % % Reference: % % ML Wolfson, HV Wright, % Algorithm 160: % Combinatorial of M Things Taken N at a Time, % Communications of the ACM, % Volume 6, Number 4, April 1963, page 161. % % Parameters: % % Input, integer N, K, are the values of N and K. % % Output, integer VALUE, the number of combinations of N % things taken K at a time. % mn = min ( k, n - k ); mx = max ( k, n - k ); if ( mn < 0 ) value = 0; elseif ( mn == 0 ) value = 1; else value = mx + 1; for i = 2 : mn value = ( value * ( mx + i ) ) / i; end end return end