Exercise 1: 1) Suppose we have to select a manager, assistant manager, and night manager from a list of 10 people. How many ways can this be done

The many ways we can select a manager, assistant manager, and night manager from a list of 10 people is:

120 possible combinations.

Step-by-step explanation:

a) Data and Calculations:

Number of selections = 3

Total number of elements to choose from = 10

This translates to 10! /(3! (10 - 3)!

10! = 3,628,800

7! = 5,040

3! = 6

Therefore, 3,628,800/6 * 5,040 = 3,628,800/30,240 = 120

We also describe this combination as 10 Choose 3 = 120.

Therefore, 120 is the total number of all possible combinations for choosing 3 elements at a time from 10 distinct elements.  Note that this does not consider the order of choosing the three elements.  In statistics and probability surveys or experiments, the formula for combinations is generally n! / (r! (n - r)!), where n is the total number of possibilities to start and r is the number of selections made.

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.