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

How many numbers between $5000$ and $10000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if no digit is repeated?

How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?

Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is

Five students are to be arranged on a platform such that the boy $B_1$ occupies the second position and the girl $G_1$ is always adjacent to the girl $G_2$. Then,the number of such possible arrangements 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 . . . . . . .