*Prob 1. **Let n _{1} = x_{1} x_{2} x_{3} and n_{2} = y_{1}y_{2} y_{3} be two 3 digit numbers. How many pairs of n_{1} and n_{2} can be formed so that n_{1} can be subtracted from n_{2} without borrowing.*

** Sol.** Clearly n

_{1}can be subtracted from n

_{2}without borrowing if y

_{i}≥ x

_{i}for i = 1, 2, 3.

Let x_{i} = r, where r = 0 to 9 for i = 2 and 3

and r = 1 to 9 for i = 1.

Now as per our requirement y_{i} = r, r +1,…. , 9.

Thus we have (10 – r) choices for y_{i}.

Hence total ways of choosing y_{i} and x_{i}