In dashcat-17 Ravi has 30 balls which he want to distribute to 3 children such a way that each of them get diff no of balls. find the no of ways he distribute the balls. For this solution is given as a+b+c=30 (a,a,a)=1 (a,a,b)= (0,0,30) to (15,15,0) = 15*3=45 MY question is aren’t the values from 0-15 “16”. Please explain.

x+y+z=30

total ordered solutions=32c2

here we want different number of balls means unordered cases

case when two are equal

so 2x+y=30
so y=30-2x

so x will vary from 0 to 15 so 16 values but this will also contain case when all are equal so remove that case so 15 value and ways to arrange them 3!/2!=3

and when all r equal=1 case

(ordered-3*when two are same-all same)
=((32c2-3*15-1)=450