Question

(1 point) how many 6-letter words that have the letter 'x' are possible? letters may be repeated, and the words don't have to be meaningful. (hint: first count the words without 'x' .)

Answer 1

The number of 6-letter words that have the letter 'x' is 0.

Step-by-step explanation:

To find the number of 6-letter words that have the letter 'x', we can first count the words without 'x'.

There are 26 letters in the alphabet, and since the words can have repeated letters, we have 26 choices for each of the 6 positions in the word. So, the total number of 6-letter words without 'x' is 26^6 = 26,^sup>6^/sup> = 308,915,776.

Now, let's find the number of 6-letter words with 'x'. Since we've already counted the words without 'x', we can subtract this number from the total number of 6-letter words (26^6) to get the answer:

Total number of 6-letter words with 'x' = Total number of 6-letter words - Total number of 6-letter words without 'x'

= 26^6 - 308,915,776

= 26^6 - 26^6

= 0

Therefore, there are 0 6-letter words that have the letter 'x'.

Answer 2

Since, there are 26 letters in total.

So, total permutations of 26 letters in the 6 letter word will be = 26*26*26*26*26*26 = 26^6

No. of letters that doesn’t include X = 26-1 =25

Permutations of letters that doesn’t include x = 25*25*25*25*25*25 = 25^6

So, total number of permutations that includes x= total permutations of 26 letters- permutation of letters that doesn’t include x

= (26^6 - 25^6) = 64,775,151