I was posed the question

"how many license plates contain at most 3 numerals followed by exactly 4 distinct letters"

I figured

3x26!-22! +

2x26!-22! +

1x26!-22!

How is this expressable or ssimplified and am I even correct

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- Dec 24th 2012, 10:51 AMlhurlbertLicense plate combinations
I was posed the question

"how many license plates contain at most 3 numerals followed by exactly 4 distinct letters"

I figured

3x26!-22! +

2x26!-22! +

1x26!-22!

How is this expressable or ssimplified and am I even correct - Dec 24th 2012, 11:01 AMPlatoRe: License plate combinations
- Dec 24th 2012, 08:22 PMSorobanRe: License plate combinations
Hello, lhurlbert!

I don't see the resoning behind your answer/

Quote:

How many license plates contain at most 3 numerals followed by exactly 4 distinct letters?

It starts with at most 3 digits.

It can havedigits: 1 way.*no*

It can have any number from 1 to 999.

. . Hence, there are 1000 choices for the numerals.

$\displaystyle \text{There are: }\,26\cdot25\cdot24\cdot23 \:=\:358,\!800\text{ possible four-letter "words"}$

. . $\displaystyle \text{with distinct letters.}$

$\displaystyle \text{Therefore, there are: }\,(1,\!000)(358,\!800) \:=\:358,\!800,\!000\text{ possible license plates.}$

- Dec 25th 2012, 03:59 AMPlatoRe: License plate combinations

As you can see the answer above differs from the one I gave.

Here is why: I read the question in such a way that the plates $\displaystyle 90ABXT~\&~090ABXT$ are different.

In other words: There is 1 way for no digits.

There are 10 ways for one digit.

There are 100 ways for two digits.

There are 1000 ways for three digits.