$_n{P_r} \div \binom{n}{r} = ..........$

Statement-$1$: $10$ identical balls can be distributed into $4$ distinct boxes in $^9C_3$ ways such that no box remains empty.
Statement-$2$: Any $3$ positions out of $9$ positions can be selected in $^9C_3$ ways.

If $^{2n}C_2 : ^nC_2 = 9:2$ and $^nC_r = 10$,then $r = $

From $5$ consonants and $5$ vowels,how many words can be formed using $3$ consonants and $2$ vowels?

$A$ question paper has two sections $A$ and $B$,in which section-$A$ has $8$ questions and section-$B$ has $6$ questions. $A$ student has to answer a total of $10$ questions,choosing at least $4$ questions from section-$A$ and at least $3$ questions from section-$B$. The number of ways a student can answer the paper is:

The number of values of $n \in N$ for which ${ }^{n+2} C_2 : { }^{n+3} C_1 = 4 : 2$ is