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.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.