If $_n{P_4} = 24 \times \binom{n}{5}$,then $n = \dots$

There are $3$ sections in a question paper and each section contains $5$ questions. $A$ candidate has to answer a total of $5$ questions,choosing at least one question from each section. Then the number of ways,in which the candidate can choose the questions,is

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is

The number of seven-digit integers,with the sum of the digits equal to $10$ and formed by using the digits $1, 2,$ and $3$ only,is

What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the four cards of the same suit?

In how many ways can $3$ letters be posted in $4$ letter boxes,if all the letters are not posted in the same letter box?