How many ordered triples of strictly positive integers (x, y, z) are solutions to the equation x + y + z = n where n is a fixed positive integer?please help

Dear student

 

if x ,y and z are positive integer.

then total number of ways = ^n-1C_3-1 = ^n-1C₂

 

Hope it helps

 

Regards

Arun

thank you so much.

 

do have a proof or something to show the same. can you please help methe proof if possible. i took an example of x+y+z=5 and i got the ans. it will be great help if you can help me with the proof