If $^n{P_r} = 840$ and $^n{C_r} = 35$,then $n$ 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

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

For which value of $n \in N$,does $n!$ have $13$ trailing zeros?

The number of numbers greater than $5000$ and less than $9000$ that are divisible by $3$,which can be formed using the digits $0, 1, 2, 5, 9$ with repetition allowed,is . . . . . . .

Five-digit numbers are formed using the digits $1, 2, 3, 4, 5, 6$,and $8$. What is the probability that they have even digits at both the ends?