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.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.