In an examination,a student has to write exams in $8$ different subjects. He is declared fail if he fails in at least one subject. The number of ways in which he can fail is

Let the digits $a, b, c$ be in $A.P.$ Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in $A.P.$ at least once. How many such numbers can be formed?

The number of ordered pairs $(m, n)$,where $m, n \in \{1, 2, 3, \ldots, 50\}$,such that $6^m + 9^n$ is a multiple of $5$ is

How many times does the digit $5$ appear when writing natural numbers from $1$ to $100$?

The value of ${}^{47}C_4 + \sum_{j=1}^5 {}^{(52-j)}C_3$ is

The digit in the unit place of the number $2009! + 3^{7886}$ is