How many license plate combinations can be made using letters and numbers?

In summary: In this problem, we have $26$ options for the first letter, and $26$ options for the second letter, and $10$ options for each of the remaining $5$ numbers, so we have:N=26\cdot26\cdot10\cdot10\cdot10\cdot10\cdot10=26^{2}10^{5}In summary, the problem is an application of the Fundamental Counting Principle, which states that the total number of options for two events is given by multiplying the number of options for each event. In this case, we have 26 options for the first letter, 26 options for the second letter, and 10 options for each of the remaining 5 numbers, giving us
  • #1
crystal1
5
0
I am unsure about which/what formulas to use for these word problems.. Here is one:

How many different 7-place license plates are possible if the first 2 places are for letters 26 letters) and the other 5 places are for numbers (0-9, 10 numbers in total)?

Any guidance/help would be greatly appreciated!
 
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  • #2
crystal said:
I am unsure about which/what formulas to use for these word problems.. Here is one:

How many different 7-place license plates are possible if the first 2 places are for letters 26 letters) and the other 5 places are for numbers (0-9, 10 numbers in total)?

Any guidance/help would be greatly appreciated!

Hi crystal,

Welcome to MHB! (Wave)

For the letters, how many choices do we have? How about for the numbers?

A nice way to count combinations is to multiply possibilities together... for example if I have two choices for the first slot and two choices for the second slot, then there are 2*2=4 choices for both slots. Same idea applies to this problem. Any thoughts? :)
 
  • #3
All I have is 26*26=676 and 10*10*10*10*10=1,000,000 but my issue is the formality of presenting my work. I am not sure which probability formula I need to use when reading statistics questions.
 
  • #4
crystal said:
All I have is 26*26=676 and 10*10*10*10*10=1,000,000 but my issue is the formality of presenting my work. I am not sure which probability formula I need to use when reading statistics questions.

That is correct! :)

There isn't a probability calculation actually, rather a counting problem. They are very closely related but to do this problem there isn't a "plug in" type formula to use.

How you present your answer depends on how the question is posed and how your teacher/professor wants you to do it. In general you can state that because there are 26 choices for the first two positions and 10 for the last 5 positions, the total number of license plate combinations is $26 \cdot 26 \cdot 10\cdot 10\cdot 10\cdot 10\cdot 10=26^2 10^5$.

If you have any more questions about how to approach a problem or how to state your solution, we'd be happy to help you out in a new thread anytime.

Glad you found us.
 
  • #5
crystal said:
All I have is 26*26=676 and 10*10*10*10*10=1,000,000 but my issue is the formality of presenting my work. I am not sure which probability formula I need to use when reading statistics questions.

This problem is an application of the Fundamental Counting Principle.

Basically, this means that if you have $a$ options you can choose for event $A$ and $b$ options you can choose for event $B$, then the number of ways $N$ that you can do events $A$ and $B$ is given by:

\(\displaystyle N=A\cdot B\)

As an example, suppose you have 4 pairs of shoes, 6 pairs of pants and 8 shirts, then the total number of distinct "outfits" you can wear is:

\(\displaystyle N=4\cdot6\cdot8=192\)
 

FAQ: How many license plate combinations can be made using letters and numbers?

What is the purpose of license plate combinations?

The purpose of license plate combinations is to uniquely identify and register a vehicle. This helps law enforcement officials and other government agencies track ownership and usage of vehicles.

How are license plate combinations determined?

License plate combinations are typically determined by a combination of letters and numbers, with each jurisdiction having its own specific rules and patterns. Some states also offer personalized or vanity plates, which allow individuals to choose their own combination of letters and numbers for an additional fee.

Can license plate combinations be reused?

In most cases, license plate combinations cannot be reused. Once a combination has been assigned to a vehicle, it is typically retired and cannot be used again. This is to ensure that each vehicle has a unique identifier.

What do the letters and numbers on a license plate mean?

The letters and numbers on a license plate are used to identify the state or jurisdiction where the vehicle is registered, as well as the specific vehicle. Some states also use letters to indicate the type of vehicle, such as commercial or personal.

Are there any restrictions or limitations on license plate combinations?

There may be restrictions or limitations on license plate combinations, such as prohibiting offensive or vulgar combinations. Additionally, some states may have specific guidelines for the number of characters allowed on a license plate or the types of characters that can be used.

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