The tens digit of the sum $1! + 4! + 7! + 10! + 12! + 13! + 16! + 17!$ is divisible by which of the following?

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

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

How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent?

$A$ 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

The number of distinct primes dividing $12! + 13! + 14!$ is