Question

x + y + z = 5,
x is not equal to y, y is not equal to z and z is not equal to x,
all x, y and z are positive integers. Possible number of outcomes are

Answer 1

so x, y, z can lie in range [0,1,2,3,4,5].

now as per given condition

x ≠ y ≠ z

let see what are the possibilities

let say x= 0 so now y + z = 5

z = 5 - y

lets take y = 1 so z = 5-1 = 4

now lets fill the all details

so for x = 0

x y z

0 1 4

0 2 3

0 3 2

0 4 1

now assume x = 1 in that case

1 + y + z =5

z = 5 -1 -y = 4- y

now we can take y = 1 as x Is already 1 also we cant take y = 2 which makes z = 2 and we know y should not be equal to y or x

this leave us only two possible value of y = 0 ,4

so for x = 1

x y z

1 0 4

1 4 0

we can see that actually first mateix getting repeated as in first if we choose y = 1 then we have x and y are 0 and 4

. so basically for each x or y or z we have 5 possible sets so total possible sets are

= 5+5+5 = 15