If $_nP_r = 30240$ and $\binom{n}{r} = 252$,then $(n, r) = \dots$

The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

Let $x$ denote the number of ways of selecting at least one ball from a bag containing $3$ identical red balls,$4$ identical blue balls,and $5$ identical green balls. Let $y$ denote the number of ways in which a student can fail in an examination,when they have to write the examination in $5$ different subjects. Then $x+y=$

The number of $4$-digit numbers that are not divisible by $5$ is:

The number of $5$-digit numbers that are not divisible by $5$ and consist of different odd digits is:

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