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 non-zero. 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?

a. 80

b. 78

c. 71

d. 69

The answer is 69.

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

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