Question

An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …., 9 such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upside down-for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?(2003)

• A. 80
• B. 78
• C. 71
• D. 69

Answer 1

The correct option is D 69

Option (d)

The available digits are 0,1,2,3……………..9. The first digit can be chosen in 9 ways ( 0 not acceptable ), the second digit can be accepted in 9 ways ( digit repetition are not allowed). Thus the code can be made in 9 $\times$ 9 =81 ways.

Now there are only four digits which can create confusion 1,6,8,9.Total number of ways can confusion arise = 4 $\times$ 3 =12

Thus required answer = 81 – 12 = 69.