Question

An elevator containing 3 people can stop at any of the five floors. What is the probability that no two people get off at the same floor? Assume that the occupants act independently and that each occupant can pick any of the five floors with equal probability.

Answer 1

Answer: The probability that no two people get off at the same floor is 0.48 or 48/100

Step-by-step explanation:

For detailed explanation, please kindly see the attached

Answer 2

Answer:

48%

Step-by-step explanation:

We have 3 people and 5 floors

We can't have two or more people leaving in the same floor.

So, the first person to leave has 5 possibilities (all 5 floors)

Then, the second person will have only 4 possibilities, as this person can't leave in the same floor as the first one.

Lastly, the third person will have only 3 options (the 3 remaining floors that weren't selected).

The total number of possible choices, without restrictions, is 5 possibilities for each person, so 5*5*5 = 125 combinations

The combinations we want is 5*4*3 = 60 combinations

So the probability of all people choosing different floors is 60/125 = 0.48 = 48%