Question

A plant manager randomly selects a can of peas from the assembly line and records whether or not the can's label is properly attached , followed by the weight of the can (as less than 14 ounces, exactly 14, or more than 14 ounces).

Counting rule: Multiple-Step Experiments, permutations, or combinations?

Number of Experimental Outcomes?

Three branches (A,B, and C) of a bank have open manager positions. Three home-office employees from a pool of five are randomly selected to fill the manager positions. The first home-office employee selected becomes the manager of branch A, the second becomes the manager of branch B, and the third becomes manager of branch C.

Counting rule: Multiple-Step Experiments, permutations, or combinations?

Number of Experimental Outcomes?

A stockbroker forms a stock portfolio for a client by randomly selecting three stock from a pool of five.

Counting rule: Multiple-Step Experiments, permutations, or combinations?

Number of Experimental Outcomes?

Answer 1

Complete Question

For each of the following experiments, identify the counting rule that is relevant for determining the number of experimental outcome.Then use the counting rules to determine the number of experimental outcome

First Experiment

A plant manager randomly selects a can of peas from the assembly line and records whether or not the can's label is properly attached , followed by the weight of the can (as less than 14 ounces, exactly 14, or more than 14 ounces).

Which is the correct Counting rule?

1) Multiple-Step Experiments

2) Permutations

3) Combinations

What is the Number of Experimental Outcomes?

Second Experiment

Three branches (A,B, and C) of a bank have open manager positions. Three home-office employees from a pool of five are randomly selected to fill the manager positions. The first home-office employee selected becomes the manager of branch A, the second becomes the manager of branch B, and the third becomes manager of branch C.

Which is the correct Counting rule?

1) Multiple-Step Experiments

2) Permutations

3) Combinations

What is the Number of Experimental Outcomes?

Third Experiment

A stockbroker forms a stock portfolio for a client by randomly selecting three stock from a pool of five.

Which is the correct Counting rule?

1) Multiple-Step Experiments

2) Permutations

3) Combinations

What is the Number of Experimental Outcomes?

Answer:

First Experiment

Counting rule: Multiple-Step Experiments

Number of Experimental Outcomes: 6

Second Experiment

Counting rule: Permutations

Number of Experimental Outcomes: 60

Third Experiment

Counting rule: Combinations

Number of Experimental Outcomes: 10

Step-by-step explanation:

The explanation of the first experiment is on the first uploaded image

For the second experiment the counting rule is permutation because from the experiment we can see that the order of selection is important

To obtain the Number of Experimental Outcomes:

We have:

`5p_(3) = (5!)/(2!)`

`= (5*4*3*2!)/(2!)`

`= 60`

For the third experiment the the counting rule is combination because the order of selection is not important

To obtain the Number of Experimental Outcomes:

We have:

`5C_(3) =(5!)/(3!2!)`

`= 10`