Question

Twenty people get into an elevator in a hotel with seven floors, and all of them get off at some point. How many different possibilities exist for how the people could get off the elevator?

Answer 1

The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.

Step-by-step explanation:

To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.

Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:

P(20, 7) = 20! / (20 - 7)!

where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.

Answer 2

The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.

Step-by-step explanation:

To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.

Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:

P(20, 7) = 20! / (20 - 7)!

where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.