The number of points in space (x, y, z)

The number of points in space (x, y, z), whose each coordinate is a negative integer such that x+y+z+12=0 is

1 Answers

2305

Shaswata Roy ·2013-02-07 04:09:39

Let a = |x|,b = |y|,c = |z|

Therefor we need to find the numbers of ways we can select 3 numbers a,b,c (a>0,b>0,c>0) such that
a+b+c=12

12 = 1+1+1+1+1+1+1+1+1+1+1+1

Whenever we select 2 "+" signs and replace them with a comma we get 3 integers p,q,r whose sum is 12.

Number of ways of selecting the 2 "+" signs from 11 ones is:
¹¹C₂=55

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