AIEEE 2011 Solved Paper

Let XA,XB,XC and XD represent number of balls present in box A,B,C and D respectively.
As no box can be empty so,
xA≥1,xB≥1,xC≥1 and XD≥1
⇒xA−1≥0,⇒xB−1≥0,⇒xC−1≥0 and ⇒xD−1≥0
tA≥0,tB≥0,tC≥0 and tD≥0
According to the question,
‌XA+XB+XC+XD=10
Now question becomes, box A, B, C, and D can have none or one or more balls and total balls are 6
From formula we know, n things can be distributed among r people in ‌n+r−1Cr−1 ways where each people can have either 0 or more things.
∴6 balls can be distributed among 4 boxes in ‌6+4−1C4−1=‌9C3 ways where each box can have either 0 or more balls.
Therefore, Statement 1 is correct. The number of ways of choosing any 3 places from 9 different places is ‌9C3 ways. But Statement - 2 is not the correct explanation of Statement -
1.