Answer :
Final answer:
There are 18280 strings of length five or less beginning and ending with "a", calculated by considering the possible strings of lengths 1 to 5 and summing their respective possibilities.
Explanation:
The question asks how many strings of length five or less, which begin and end with the letter "a", can be formed using only lowercase alphabets. To solve this, consider the lengths of the strings that can be formed: 1, 2, 3, 4, and 5.
- For a string of length 1, there is only 1 string: "a".
- For a string of length 2, it must be "aa", hence there is 1 option.
- For a string of length 3, there are 26 options for the middle letter, so 26 strings can be formed.
- For a string of length 4, the second and third positions can each be filled by any of the 26 letters, resulting in 26 * 26 options.
- For a string of length 5, the three letters between the leading and ending "a" have 26 options each, giving us 26^3 possibilities.
You sum these numbers to find the total amount:
1 (length 1) + 1 (length 2) + 26 (length 3) + 26^2 (length 4) + 26^3 (length 5) = 1 + 1 + 26 + 676 + 17576 = 18280
Therefore, there are 18280 strings of length five or less that begin and end with the letter "a". The correct answer is not listed among the provided options.
