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- An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, ….
Question 1:
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 upsidedown-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
Feedback 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 (digits repetition not allowed).
Thus, the code can be made in 9 × 9 = 81 ways.
Now there are only 4 digits 1, 6, 8, 9 which can create confusion.
Hence, the total number of codes which create confusion are = 4 × 3 = 12.
Out of these 12 codes 69 and 96 will not create confusion.Hence, in total 12 – 2 = 10 codes will create confusion.
Hence, the total codes without confusion are 81 – 10 = 71.
The first digit can be chosen in 9 ways (0 not acceptable), the second digit can be accepted in 9 ways (digits repetition not allowed).
Thus, the code can be made in 9 × 9 = 81 ways.
Now there are only 4 digits 1, 6, 8, 9 which can create confusion.
Hence, the total number of codes which create confusion are = 4 × 3 = 12.
Out of these 12 codes 69 and 96 will not create confusion.Hence, in total 12 – 2 = 10 codes will create confusion.
Hence, the total codes without confusion are 81 – 10 = 71.
D. 69
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