Math Question - Permutations and Fundamental Counting

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Kaiyeetus

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I have no idea how to go about solving number 2. I think I figured out part a but everything else is very confusing. I just learned the formulas [math]_nP_r[/math] and [math]n!/(n-r)![/math] for non repeating objects and [math]n!/r_1!r_2!r_3!...[/math] for repeating objects. But I don't know how to use these formulas to apply to question 2.


Any help would be so so so appreciated. Screen Shot 2022-05-05 at 5.05.07 PM.png
 
Kaiyeetus said:
I have no idea how to go about solving number 2. I think I figured out part a but everything else is very confusing. I just learned the formulas [math]_nP_r[/math] and [math]n!/(n-r)![/math] for non repeating objects and [math]n!/r_1!r_2!r_3!...[/math] for repeating objects. But I don't know how to use these formulas to apply to question 2. Any help would be so so so appreciated.
Click to expand...
For a) [imath]10+26=36[/imath] so there are thirty-six symbols from which to use six: [imath]_{36}\mathscr{P}_6[/imath]
For part b) [imath](26)^3(10)^3[/imath] Why and/or How?

[imath][/imath][imath][/imath][imath][/imath]
 
What is wrong with the people who write math textbooks? Apparently, they do not know the difference between a decimal digit and a number.
 
JeffM said:
What is wrong with the people who write math textbooks? Apparently, they do not know the difference between a decimal digit and a number.
Click to expand...
What are you saying?
 
There are a total of 36 characters

2a)
How many characters do you get to choose from for the 1st position of the license plate?
How many characters do you get to choose from for the 2nd position of the license plate?
How many characters do you get to choose from for the 3rd position of the license plate?
How many characters do you get to choose from for the 4th position of the license plate?
How many characters do you get to choose from for the 5th position of the license plate?

2b)
How many characters do you get to choose from for the 1st position of the license plate?
How many characters do you get to choose from for the 2nd position of the license plate?
How many characters do you get to choose from for the 3rd position of the license plate?
How many characters do you get to choose from for the 4th position of the license plate?
How many characters do you get to choose from for the 5th position of the license plate?

2c)
How many characters do you get to choose from for the 1st position of the license plate?
How many characters do you get to choose from for the 2nd position of the license plate?
How many characters do you get to choose from for the 3rd position of the license plate?
How many characters do you get to choose from for the 4th position of the license plate?
How many characters do you get to choose from for the 5th position of the license plate?

2d)
How many characters do you get to choose from for the 1st position of the license plate?
How many characters do you get to choose from for the 2nd position of the license plate?
How many characters do you get to choose from for the 3rd position of the license plate?
How many characters do you get to choose from for the 4th position of the license plate?
How many characters do you get to choose from for the 5th position of the license plate?
 
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