# Math Help - help me which counting is correct

1. ## help me which counting is correct

How many strings are there of four lowercase letters that have the letter x in them?
which of the following answer is correct?
1) 1x26x26x26 = $26^3 = 17576$
2) $26^4 - 25^4 = 66351$

2. Originally Posted by zpwnchen
How many strings are there of four lowercase letters that have the letter x in them?
which of the following answer is correct?
1) 1x26x26x26 = $26^3 = 17576$
2) $26^4 - 25^4 = 66351$

$26^4 - 25^4 = 66351$ is the number of four letters strings which contain at least one x.
Is that what the question means.

$(4)25^3 = 62500$ is the number of four letters strings which contain exactly one x.

3. Originally Posted by Plato
$(4)25^3 = 62500$ is the number of four letters strings which contain exactly one x.
can you tell me why you multiply with 4? what is the concept behind?

4. You multiply by 4 because you have 4 ways to place x:

x _ _ _
_ x _ _
_ _ x _
_ _ _ x

5. Originally Posted by zpwnchen
can you tell me why you multiply with 4? what is the concept behind?