I'm having the following assignment:
For which positive integer $n$ will the equations $ x_1 + x_2 + x_3 + \ldots + x_{19} = n \tag{1}$ $ y_1 + y_2 + y_3 + \ldots + y_{64} = n \tag{2}$ have the same number of positive integer solutions?
I've gotten this far, with the help of notes from my teachers lectures. Though, I have been searching and looking for the answer to the following question:
How come that the following is true? Where does the $n$ disappear, and how can it be substituted with substracting one?
$\binom{n-1}{n-64} = \binom{n-1}{64-1} = \binom{n-1}{63}$
I'm thankful for any help I can get to understand this better!
Thanks, Z