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An intelligence agency forms a code of two distinct digits selected from 0, 1, 2,....., 9 such that the first-digit of code is non-zero. The code, handwritten on a slip, can however potentially create confusion when read upside down, for examples the code 91 may appear as 16. how many codes are there for which no such confusion can arise?
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- 80
- 78
- 71
- 69
Correct Option: D
The available digits are 0, 1, 2,...., 9. The first digit can be chosen in 9 ways (0 not acceptable), the second digit can be accepted in 9 ways (digit repetition not allowed). Thus, the code can be made in 9 x 9 = 81 ways.
Now, there are only 4 digits which can create confusion 1, 6, 8, 9. The same can be given in the following ways
Total number of ways confusion can arise
= 4 x 3 = 12
Thus, the ways in which no such confusion arise = 81-12 =69
