The number of ways of forming a queue of $4$ boys and $3$ girls such that all the girls are not together,is:

Four speakers will address a meeting where speaker $Q$ will always speak before $P$. Then,the number of ways in which the order of speakers can be prepared is

Find the number of arrangements of the letters of the word $BANANA$ in which the two $N$'s do not appear together.

Among the $4$-digit numbers formed using the digits $0, 1, 2, 3, 4$ where repetition of digits is allowed,the number of numbers which are divisible by $4$ is:

The number of $4$ letter words that can be formed with the letters in the word $EQUATION$ with at least one letter repeated is

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 . . . . . . .