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Question: Let n<sub>1</sub> = x<sub>1</sub> x<sub>2</sub> x<sub>3</sub> and n<sub>2</sub> = y<sub>1</sub> y<su...

Let n1 = x1 x2 x3 and n2 = y1 y2 y3 be two 3-digit numbers, then the pairs of n1 and n2 can be formed so that n1 can be subtracted from n2 without borrowing is –

A

55.54

B

45.55

C
  1. (55)2
D
  1. (45)2
Answer
  1. (55)2
Explanation

Solution

Here, n1 = x1 x2 x3 and n2 = y1 y2 y

Ž n1 can be subtracted from n2 without borrowing

if yi ³ xi for i = 1, 2, 3.

\ Let xi = r Ž

\ yi = r, r + 1, ……, 9.

Thus, for y1, y2 and y3 we have (10 – r) choices each

Ž Total number of ways for choosing yi and xi

= {∑r=09(10−r)}\left\{ \sum_{r = 0}^{9}{(10 - r)} \right\}·{∑r=09(10−r)}\left\{ \sum_{r = 0}^{9}{(10 - r)} \right\}

= 45 · 55 · 55 = 45 · (55)2

Hence (3) is correct answer.