How many $3$-digit numbers are there,with no digits repeated?

$3$ boys and $3$ girls are to be seated around a circular table. Among the boys,$X$ does not want any girl as a neighbour,and among the girls,$Y$ does not want any boy as a neighbour. How many such arrangements are possible?

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

$A$ teacher of a class wants to set $1$ question from each of $2$ exercises in a book. If there are $15$ and $12$ questions in the $2$ exercises respectively,then in how many ways can the $2$ questions be selected?

In a train,there are $5$ vacant seats. In how many ways can $3$ passengers sit on these seats?

In a touring cricket team,there are $16$ players in all,including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players can be chosen from these,such that each team includes exactly $3$ bowlers and $1$ wicket-keeper?