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.
Always satisfy the Prime Directive of getting the right answer above all else.