Question

a man is asked say a three digit number
what is the probability of all three digits be same
what is the probability of getting sum of the digite being 26
what is the probability of getting last digit be 0
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Answer 1

Answer:

Well, you can solve this using theory of congruence too, but i will prefer the easier method, it’s quite trivial to note that the last digit of powers of 8 get repeated at regular intervals.

notice last digit in each case:-

8^1 = 8

8^2 = 64

8^3 = …2

8^4 = ..6 (when power mod 4 = 0)

8^5 = …8 (when power mod 4 = 1)

8^6 =…4 (when power mod 4 = 2)

8^7 = …2 (when power mod 4 = 3)

8^8 = ….6 (when power mod 4 = 0)

and so on.. so the last digits gets repeated at regular intervals of 4.

divide 2016 by 4, you will get a remainder 0, so last digit will be 6.