An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?
Choose the correct option
A) 90  B) 80  C) 40  D) 50  E) 89
Total digits that can be formed = 10C1 * 10C1 = 100.   The digits that still remain digits when turned upside down are 0, 1, 6, 8 and 9.   So codes that can create confusion are:   01, 06, 08, 09   10, 16, 18, 19   60, 61, 66, 68 (69 would still be 69 when inverted)   80, 81, 86, 89   90, 91, 98, 99 (96 would still be 96 when inverted)   There are 20 such numbers.   Required numbers = 100 - 20= 
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
80   ANSWER:80
<result>B</result>
An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?