From a collection of $20$ consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

Let $A$ be a set containing $n$ elements. $A$ subset $P$ of $A$ is chosen, and the set $A$ is reconstructed by replacing the elements of $P$. $A$ subset $Q$ of $A$ is chosen again. The number of ways of choosing $P$ and $Q$ such that $Q$ contains just one element more than $P$ is

In a circus,there are $10$ cages for accommodating $10$ animals. Out of these,$4$ cages are so small that $5$ out of the $10$ animals cannot enter them. In how many ways is it possible to accommodate the $10$ animals in these $10$ cages?

$(2n + 1) (2n + 3) (2n + 5) \dots (4n - 1)$ is equal to :

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 $(7!)$)

$A$ question paper is divided into two parts $A$ and $B$,and each part contains $5$ questions. The number of ways in which a candidate can answer $6$ questions,selecting at least two questions from each part,is: