A dormitory has 40 students---12 sophomores, 8 juniors, and 20 seniors. Which of the following is equal to the number of ways to

Answer:

The number of arrangements is equal to

Step-by-step explanation:

The multiplication principle states that if a first task can be done in n1 different ways, a second task can be performed in n2 different ways... and extending this logic for i tasks gives us the total ways as

n1 x n2 x... x ni

Moreover, with n-elements arranged in a line, the total arrangements possible are n! which is referred to as n-factorial.

As an example: If we wish to arrange 4 distinct items in a row.

The total ways to arrange this is ways.

Applying the multiplication principle and n-factorial number:

The number of ways to line up all 40 for a photograph, with all 12 sophomores to the left, all 8 juniors in the center, and all 20 seniors to the right is: The total configurations for the 12 sophomores in a row multiplied by the arrangements for the 8 juniors and finally multiplied by the total ways to align all 20 seniors in a row ⇒