If $^n{P_4} = 30 \times {^n}{C_5}$,then $n = $

$A$ bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively,until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is $14400$,then $n$ is equal to

Five-digit numbers are formed using the digits $1, 2, 3, 5, 7$ with repetitions and are written in descending order with serial numbers. For example,the number $77777$ has serial number $1$. Then the serial number of $35337$ is $.........$.

The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is

The remainder of $n^4-2n^3-n^2+2n-26$ when divided by $24$ is:

The number of words that do not start and end with vowels,formed using all the letters of the word $'UNIVERSITY'$ such that all vowels are in alphabetical order,is