The number of integers,greater than $7000$,that can be formed using the digits $3, 5, 6, 7, 8$ without repetition is:

How many numbers greater than a million can be formed with the digits $2, 3, 0, 3, 4, 2, 3$?

In how many ways can $8$ distinct toys be distributed among $5$ children?

How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?

${ }^{20}P_5 - { }^{19}P_5 = $

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 . . . . . . .