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 a. `1/5` b. `1/5(9/(10))^3` c. `(3/5)^4` d. none of these

Explanation

The possible options for the last digits are `0, 1, 2, 3, 4, 5` only (`2` out of `10`)

`therefore` No. of possible options for second last digit are `9` out of `10` (cant be equal to last digital so `10-1`)

Similarly,

No. of possible options for third last digit are 9 out of 10, fourth last digit are `9` out of `10`

For first digit there are `9-1=8` due to constraint out of `9` nos.

`therefore` Probability that the number is divisible by `5` and no two consecutive digits are identical

`=8/9 * 9/10 * 9/10 * 9/10 * 2/10 = (3/5)^4`