Problem 53

Problem 53
Filename: prob53.m

% Problem 53

% There are exactly ten ways of selecting three from five, 12345:
% 
% 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
% 
% In combinatorics, we use the notation, 5C3 = 10.
% 
% In general,
% 
% nCr =	
% n!
% r!(nr)!
% ,where r  n, n! = n(n1)...321, and 0! = 1.
% It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
% 
% How many, not necessarily distinct, values of  nCr, for 1  n  100, are greater than one-million?

count = 0;
for i=1:100
  for j=1:i
    if nchoosek(i,j) > 1000000
      count = count + 1;
    end
  end
end

count

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