Question

Seven people enter the elevator on the first floor of a 12 story building. What is the probability that no two will get off on the same floor? (you may assume that all floors are equally likey and no one gets off the elevator before it)

Answer 1

Answer:

The probability that no two people will get off on the same floor is 0.1114.

Step-by-step explanation:

The number of people in the elevator is 7.

The number of floors is 12.

Then the arrangement in which 7 people can get off on the 12 floors in $_{12} P_{7}$.

The total number of ways in which the 7 people can get off on the 12 floors is $12^{7}$.

The probability that no two people will get off on the same floor is:

$=\frac{_{12}P_{7}}{12^{7}} = \frac{3991680}{35831808} =0.1114$

Thus, the probability that no two people will get off on the same floor is 0.1114.