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 non-zero. The code, handwritten on a slip, can however potentially create confusion when read upside down i.e., 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. $69$

Answer 1

The correct option is C $71$

The digits which create confusion are 0, 1, 6, 8, 9.
The total number of two-digit codes having distinct digits and first digit non-zero.

1st place

2nd place

9 option 9 options ( one digit is
(1 to 9) already used out of 1 to 9 and 0 is
included)
= $9\times 9$ =81 such codes
Total number of two digit codes which can create confusion.

1st digit

2nd digit

4 options 4 options
(1, 6, 8 or 9) (one digit is already used out or
1, 6, 8 and 9 and 0 is
also included )
=$4\times 4$=16
But these 16 two-digit codes include 69 and 96, which create no confusion. Apart from these, 10, 60, 80 and 90 are such two digit codes as create no confusion because these codes are no expected.
Hence total number of two-digit codes which create no confusion
=81-16+6=71