The number of $5$ digit telephone numbers having at least one of their digits repeated is

There are $4$ men and $5$ women in Group $A$,and $5$ men and $4$ women in Group $B$. If $4$ persons are selected from each group,then the number of ways of selecting $4$ men and $4$ women is:

$A$ question paper has $3$ parts $A, B, C$. Part $A$ contains $7$ questions,part $B$ contains $5$ questions,and part $C$ contains $3$ questions. If a candidate is allowed to answer not more than $4$ questions from part $A$,not more than $3$ questions from part $B$,and not more than $2$ questions from part $C$,then the number of ways in which a candidate can answer exactly $7$ questions is

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is

In how many ways can $3n$ distinct objects be distributed equally among $3$ persons?

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is