. An elevator in a building starts with five passengers and stops at seven floors. Say every passenger is equally likely to get off at each floor and all the passengers leave independently of each other. a. How many ways are there for the passengers to be assigned a floor? b. How many ways are there for the passengers to be assigned a floor but no two passengers are on the same floor?

There are 16807 number of ways the passengers to be assigned a floor and there are 2520 number of ways the passengers to be assigned a floor but no two passengers are on the same floor.

Given that an elevator starts with five passengers and stops at the seven floors of a building.

From the given information, the total number of floors n=7.

The number of passengers r = 5.

(a) Compute the number of ways that 5 passengers can be assigned to seven floors.

Here, repetition is allowed.

From the known information, if r numbers are selected from n number of observations then the total number of observations that can be drawn from n number of observations is [tex]n^r[/tex].

If 5 passengers can be assigned to seven floors is 7⁵ = 16807.

(b) Compute the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor.

Here, repetition is not allowed.

If 5 passengers can be assigned to seven floors but no two passengers are on the same floor is 7x6x5x4x3 = 2520.

Hence, the number of ways that 5 passengers can be assigned to seven floors is 16807, and the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor is 2520.

Learn about permutation from here brainly.com/question/16554742

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