Question

There are 8 floors on a building including the ground floor. If 4 persons enter the lift in the ground floor the number of ways in which they get down the lift if no two persons come out of the lift at the same floor is

• A. ${}^7{C}_4$
• B. $7^4$
• C. ${}^7{P}_4$
• D. $4^7$

Answer 1

Answer: (C)

${}^7{P}_4$

$\Rightarrow$ They have 7 floors to get down on, So, the $1^{st}$ person may choose any one of the 7 floors to get down. The $2^{nd}$ one may choose any one of the 6 remaining and so on.
$\Rightarrow$ The total $=7\ast 6\ast 5\ast 4$
${=}^7{P}_4$