$^nC_r \div ^nC_{r-1} = $

The number of ways in which one or more balls can be selected out of $10$ white,$9$ green,and $7$ blue balls is:

$A$ student has to answer $10$ out of $13$ questions in an examination,choosing at least $5$ questions from the first $6$ questions. The number of choices available to the student is:

Out of $7$ consonants and $4$ vowels,the number of words consisting of $3$ consonants and $2$ vowels that can be formed is:

Compute $\frac{8!}{6! \times 2!}$

If $\binom{2n}{3} : \binom{n}{2} = 44 : 3$ and $\binom{n}{r} = 15$,then $r = \dots$