Out of $6$ books, in how many ways can a set of one or more books be chosen
$64$
$63$
$62$
$65$
Value of $r$ for which $^{15}{C_{r + 3}} = {\,^{15}}{C_{2r - 6}}$ is
If $^n{C_{12}} = {\,^n}{C_6}$, then $^n{C_2} = $
The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is
The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets themselves such that they get consecutive blocks of $5, 3 $ and $2$ tickets is
In an examination, a question paper consists of $12$ questions divided into two parts i.e., Part $\mathrm{I}$ and Part $\mathrm{II}$, containing $5$ and $7$ questions, respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?