Can someone help me understand why, calling n to the number of possible solutions to the below equation and constraint: $$ x_{1} + ... + x_{k} = 100 ;\textit{ }x_{i}\geq 1 \textit{ for }1 \leq i \leq k $$ n is: $$ n= \binom{99}{k-1} $$
It is used in my text book to reach the solution of a broader problem, but I can't see exactly why n takes that value.
Thank you!
