The total number of $5$-digit telephone numbers that can be formed such that at least one digit is repeated is .... (The first digit cannot be $0$).

If $a + b + c = 50$ and $a, b, c$ are non-negative even integers,then the greatest value of $ab^2c$ is:

The number of four-digit numbers formed by using the digits $0, 2, 4, 5$ (without repetition) which are not divisible by $5$ is:

If ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways,in which a team of $3$ students can be randomly selected from this group such that there is at least one boy and at least one girl in each team,is $1750$,then $n$ is equal to

$A$ five-digit number divisible by $3$ has to be formed using the numerals $0, 1, 2, 3, 4,$ and $5$ without repetition. The total number of ways in which this can be done is: