HOTS : Permutations & Combinations

Prob 1.    Let n1 = x1 x2 x3 and n2 = y1y2 y3 be two 3 digit numbers. How many pairs of n1 and n2 can be formed so that n1 can be subtracted from n2 without borrowing.

Sol.   Clearly  n1 can be  subtracted from n2 without  borrowing  if yi ≥ xi  for  i = 1, 2, 3.

Let xi = r, where  r = 0  to 9  for   i = 2 and 3

and  r = 1 to 9  for  i = 1.

Now as per our requirement yi = r, r +1,…. , 9.

Thus we have (10 – r) choices for  yi.

Hence total ways of choosing yi  and  xi

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