If ${}^n{P_5} = 20 \times {}^n{P_3}$,then $n = $

How many words,with or without meaning,can be formed using the letters of the word $MONDAY$,assuming that no letter is repeated,if $4$ letters are used at a time?

In a $12$-storied building,$3$ persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

In how many ways can the letters of the word $ASSASSINATION$ be arranged so that all the $S$'s are together?

Let $b_{1} b_{2} b_{3} b_{4}$ be a $4$-element permutation with $b_{i} \in \{1, 2, 3, \ldots, 100\}$ for $1 \leq i \leq 4$ and $b_{i} \neq b_{j}$ for $i \neq j$,such that either $b_{1}, b_{2}, b_{3}$ are consecutive integers or $b_{2}, b_{3}, b_{4}$ are consecutive integers. Find the number of such permutations.