Combination Question - Real Life Example # of Driving Modes

[QuickQuestion123]

Hey,

Let's assume I have a car with the following 4 driving modes

1. Suspension
2. Handling
3. Transmission
4. Efficiency

Each driving mode has 3 possible sub settings (Low, Medium, High)

Question - How many possible driving modes can I have.

We would eliminate repetition and order does not matter?

Formula:​

n = 12?
r = 4 ?

 

[stapel]

Let's assume I have a car with the following 4 driving modes

1. Suspension
2. Handling
3. Transmission
4. Efficiency

Each driving mode has 3 possible sub settings (Low, Medium, High)

Question - How many possible driving modes can I have.

We would eliminate repetition and order does not matter?

Formula:​

n = 12?
r = 4 ?

How is the assignment defining "modes"? If it's using "mode" as in the first line above, then there are "the following 4 driving modes", so there are four modes. If it's using "mode" to refer to "mode, plus sub-setting", then each first-line "mode" has three sub-settings, for a total of how many mode-plus-sub-setting values? (Hint: Multiply.)

 

[ksdhart2]

That's formula's not even close to what you'd want for this. That formula is "12 choose 4." Essentially, that gives the result for if you had 12 marbles in a bag and picked 4 at random. If we applied that here, you might end up with "Low Suspension," "Medium Handling," "High Handling," and "High Efficiency." But that's not a valid driving arrangement. Instead, it might be best to go back to the drawing board and think about what the problem is asking. You can pick one of three options for Suspension. Regardless of which you picked, you then have three options for Handling. If those two were the only modes, how many possible arrangements would there be? How did you arrive at that answer? Can you see how to apply the same logic to the case where you're considering all four modes?

 

[QuickQuestion123]

The later - 3x3x3x3 = 81

Why would the combination formula not work?

 

[pka]

Let's assume I have a car with the following 4 driving modes

1. Suspension
2. Handling
3. Transmission
4. Efficiency

Each driving mode has 3 possible sub settings (Low, Medium, High)
Question - How many possible driving modes can I have?

You are wildly out from understanding this question.
Think of a \(\displaystyle 4 \times 3\) matrix. The rows are the driving modes , the columns are the setting.
So your question comes down to:
How many ways can you place exactly one X in each row?

 

[pka]

The later - 3x3x3x3 = 81

Why would the combination formula not work?

Your answer is correct even to my model.
Combinations just have absolutely nothing to do with this question.
It is probability not anything you have done but has everything with how you have been taught.
Formulas are absolutely useless if you don't understand exactly what is being counted.