Q: How many solutions are there to:

x1 + x2 + x3 + x4 +x5 = 50 for integers xi >= 1

What I've done:

Rewrite as: (x1 - 2) + (x2 - 2) + (x3 - 2) + (x4 - 2) + (x5 - 2) = 40

My answer: The number of solutions isC(40 + 5 - 1 , 40 ) = 135751

The answer has been given as 130905. Any idea where I have gone wrong?