Two 4-digit numbers are to be formed such that the sum of the number is also a 4-digit number and in no place the addition is with carrying the number of ways of forming the number under above conditions is
I am taking it that you mean the sum of the two 4 digit numbers must be a 4 digit number and in no column can there be a carry.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.