In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?

How many words can be formed using the letters of the word $ARRANGE$ such that the consonants appear in alphabetical order?

How many words can be formed using the letters of the word '$ARTICLE$' if the vowels always occupy odd positions?

If ${}^n P_4 = 1680$,then $n =$

How many $4$-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that at least one digit is $1$?

Three persons enter a lift at the ground floor. The lift goes up to the $10^{\text{th}}$ floor. If the lift does not stop at the $1^{\text{st}}$,$2^{\text{nd}}$,and $3^{\text{rd}}$ floors,the number of ways in which the three persons can exit the lift at three different floors is equal to . . . . . . .