The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is

The number of permutations of the letters $a_1, a_2, a_3, a_4, a_5$ in which the first letter $a_1$ does not occupy the first position and the second letter $a_2$ does not occupy the second position is:

The number of natural numbers less than $10000$ which are divisible by $5$ and in which no digit is repeated is:

If $\frac{{}^{n + 2}C_6}{{}^{n - 2}P_2} = 11$,then $n$ satisfies the equation

There are $4$ men and $5$ women in Group $A$,and $5$ men and $4$ women in Group $B$. If $4$ persons are selected from each group,then the number of ways of selecting $4$ men and $4$ women is:

$A$ question paper contains $4$ questions,each having $4$ alternative answers. The number of ways that a candidate can answer one or more questions is