If $^{n}P_{4} = 24 \times ^{n}C_{5}$,then the value of $n$ is

How many numbers can be formed from the digits $1, 2, 3, 4$ when repetition is not allowed?

There are three sections in a question paper,each containing $4$ questions. If a candidate has to answer only $5$ questions from this paper without leaving any section,then the number of ways the candidate can make the choice of questions 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?

Number of $4-$digit numbers (the repetition of digits is allowed) which are made using the digits $1, 2, 3$ and $5$,and are divisible by $15$,is equal to $............$.

Three letters are chosen at random from the letters of the word $VARIABLE$ and all possible three-letter words (with or without meaning) are formed with them. Then the probability of getting a three-letter word having a consonant as its middle letter is