How many numbers consisting of $5$ digits can be formed in which the digits $3, 4$ and $7$ are used only once and the digit $5$ is used twice?

Let $A = \{a_1, a_2, a_3, ..., a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)

In a plane,there are $10$ points,out of which $4$ are collinear. The number of triangles that can be formed by joining these points is:

The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is

How many $3$-digit numbers can be formed using $0, 1, 3, 5, 7$ when repetition is allowed?