How many 5-letter words that have the letter 'x' are possible?

Question

Letters may be repeated, and the words don't have to be meaningful. (Hint: First count the words without 'x' .)

Answer 1

To make this easier to solve, first find the number of 5 letter words that do not have any X's, then subtract that number from the total possible number of 5 letter words.

The number of letters in the alphabet that are not X is 25.  The number of 5 letter words in which all five letters are not X's is 25^5=9,765,625.

Now find the total number of all possible 5 letter words.  Since each letter could be 26 different things, the total number of words is 26^5=11,881,376.

Finally, find the difference between the two numbers: 11,881,376 - 9,765,625 = 2,115,751.  There are 2,115,751 different 5 letter words that contain at least one X!

Answer 2

ALL of the 5 letter words that have the letter x are possible, not 1 more nor 1 fewer.