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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

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 

Grade:12th pass

2 Answers

Arun
25757 Points
4 years ago
Dear student
 
if x ,y and z are positive integer.
then total number of ways = n-1C3-1 = n-1C2
 
Hope it helps
 
Regards
Arun
shiya
14 Points
4 years ago
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 
 

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