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

In how many ways can $16$ rupees be divided among $4$ persons such that no person receives less than $3$ rupees?

$^{n-1}C_3 + ^{n-1}C_4 > ^nC_3$,then the value of $n$ is

$A$ question paper consists of two sections having $3$ and $4$ questions respectively. The following note is given on the paper: "It is not necessary to attempt all the questions. One question from each section is compulsory". In how many ways can a candidate select the questions?

There are $7$ identical white balls and $3$ identical black balls. The number of distinguishable arrangements in a row of all the balls,so that no two black balls are adjacent is

The total number of ways of selecting $4$ letters from all the letters of the word $TSEAMCET$ is