Answer:
Step-by-step explanation:To find the number of strings of lowercase letters that contain the letter x, we can use the concept of counting techniques in combinatorics.
Strings of 2 lowercase letters with the letter x:
There are 26 lowercase letters in the English alphabet, including x. To count the number of strings of 2 lowercase letters that contain x, we can fix the position of the x and then count the number of ways to fill the second position with any of the remaining 25 letters.
Therefore, there are 25 ways to choose the second letter of the string. Thus, the total number of strings of 2 lowercase letters that have the letter x in them is:
25
Strings of 4 lowercase letters with the letter x:
Using a similar approach, we can fix the position of the letter x and then count the number of ways to fill the remaining 3 positions with any of the 25 remaining lowercase letters.
Therefore, there are 25 × 25 × 25 ways to fill the remaining 3 positions after fixing the position of the x. Thus, the total number of strings of 4 lowercase letters that have the letter x in them is:
25 × 25 × 25 = 15,625
Strings of k lowercase letters with the letter x:
Following the same logic as above, we can fix the position of the x and then count the number of ways to fill the remaining k-1 positions with any of the 25 remaining lowercase letters.
Therefore, there are 25^(k-1) ways to fill the remaining k-1 positions after fixing the position of the x. Thus, the total number of strings of k lowercase letters that have the letter x in them is:
25^(k-1)
So, the number of strings of 2 lowercase letters with the letter x is 25, the number of strings of 4 lowercase letters with the letter x is 15,625, and the number of strings of k lowercase letters with the letter x is 25^(k-1).