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

[crystal1]

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!

 

[Jameson]

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? :)

 

[crystal1]

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.

 

[Jameson]

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.

 

[MarkFL]

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:

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