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
Hello, lhurlbert!
I don't see the resoning behind your answer/
How many license plates contain at most 3 numerals followed by exactly 4 distinct letters?
It starts with at most 3 digits.
It can have no digits: 1 way.
It can have any number from 1 to 999.
. . Hence, there are 1000 choices for the numerals.
$\displaystyle \text{There are: }\,26\cdot25\cdot24\cdot23 \:=\:358,\!800\text{ possible four-letter "words"}$
. . $\displaystyle \text{with distinct letters.}$
$\displaystyle \text{Therefore, there are: }\,(1,\!000)(358,\!800) \:=\:358,\!800,\!000\text{ possible license plates.}$
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.