Find the number of ways of selecting $4$ pens and $3$ pencils from a packet of $8$ pens and $5$ pencils.

$A$ committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?

An engineer is required to visit a factory for exactly $4$ days during the first $15$ days of every month,and it is mandatory that no two visits take place on consecutive days. The number of all possible ways in which such visits to the factory can be made by the engineer during $1-15$ June $2021$ is:

If $^{n-1}C_r = (k^2 - 3) \cdot ^nC_{r+1}$,then an interval containing the values of $k$ is

$A$ student is allowed to select at least $(n+1)$ books but not all books from a collection of $(2n+1)$ books. If the total number of ways in which he can select these books is $255$,then the number of books in that collection is

Out of $7$ consonants and $4$ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2$ vowels, is