JEE Advanced Mathematics question

A five-digit number is written down at random. The probability that the number is divisible by 5 and no two consecutive digits are identical, is

Answer: (D)

Solution

(the first digit cannot be 0).

Fill the digits from the right, (units) back to :

- : 2 ways; - : 9 ways; : 9 ways; : 9 ways; - and : **8 ways if , but 9 ways if .**

So \cd$

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Question ID VK-109730