In how many ways can $6$ '$+$' signs and $4$ '$*$' signs be arranged in a row such that no two '$*$' signs occur together?

There are $10$ intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at $3$ of these intermediate stations so that no two of these halting stations are consecutive is:

In an election,$3$ members are to be elected from $6$ candidates. $A$ voter can cast their vote for any number of candidates but not more than the number of candidates to be elected. In how many ways can a voter cast their vote?

If $^nC_4$, $^nC_5$ and $^nC_6$ are in arithmetic progression ($A$.$P$.), then the value of $n$ is...

If $\binom{15}{3r} = \binom{15}{r+3}$,then $r = \dots$

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.