A natural number is selected at random from $1$ to $1000.$ Then the probability that non-zero digits appear at most once is

Q. A number is selected at random then the probability such that no two identical digits appear together.

Q. Four digit numbers are formed using each of the digits $1,2,.......,8$ only once. One number from them is picked at random then the probability that the selected number contains unity is

Q. A coin weighted so that $P\left(H\right)=2/3$ and $P\left(T\right)=1/3$ is tossed. If head appears, then a number is selected at random from the number $1$ through $9$, If tail appears, then the number is selected at random from the numbers $1$ through $5$. Find the probability $p$ that an even number is selected?

Q. One ticket is selected at random from $50$ tickets numbered $00,01,\mathrm{02....49}$. Then the probability that the sum of the digits on the selected ticket is $8$, given that the product of these digits is zero, is

Q. One ticket is selected at random from $50$ tickets numbered $00,01,02,...,49$. Then the probability that the sum of the digits on the selected ticket is $8$, given that the product of these digits is zero, equals