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

AI Thread Summary
To determine the number of different 7-place license plates with the first two places for letters (26 options) and the last five for numbers (10 options), the calculation involves multiplying the possibilities. The total combinations can be calculated as 26^2 for the letters and 10^5 for the numbers, resulting in a formula of 26^2 * 10^5. This approach is based on the Fundamental Counting Principle, which states that the total number of outcomes is the product of the choices for each event. Proper presentation of the solution will depend on the specific requirements of the assignment or instructor.
crystal1
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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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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? :)
 
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.
 
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.
 
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:

$$N=A\cdot B$$

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:

$$N=4\cdot6\cdot8=192$$
 
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