The number of $4$-digit numbers that can be formed from the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that each number contains the digit $1$ is:

The number of $5$-digit natural numbers such that the product of their digits is $36$ is:

The number of $5$-digit odd numbers greater than $40,000$ that can be formed by using the digits $3, 4, 5, 6, 7, 0$ such that at least one of its digits is repeated is:

$A$ five-digit number divisible by $3$ has to be formed using the numerals $0, 1, 2, 3, 4,$ and $5$ without repetition. The total number of ways in which this can be done is:

Numbers between $1$ and $10,000$ are formed using the digits $2$ and $3$ exactly once and the digit $4$ twice. If the numbers thus formed are arranged in increasing order and $x, y$ represent the ranks of $4324$ and $324$ respectively,then $x-y=$

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