Using the ordinary alphabet and allowing repeated letters, find the number of words of length 8 that begin and end with T.
If any combination of letters counts as a word, then there are 26 ways to choose each of the six letters between the two t's.
So, there are 26^6 = 308915776 ways to make 8-letter words
To find the number of words of length 8 that begin and end with the letter T, we can consider that the remaining 6 positions can be filled with any letter from the ordinary alphabet, including repeated letters.
Since all arrangements of these 6 positions will be valid words, we can use the concept of permutations with repetition to determine the total number of words.
Permutations with repetition formula: n^r
Where:
- n is the number of options for each position, which in this case is 26 (the size of the ordinary alphabet).
- r is the number of positions to be filled, which in this case is 6.
Using this formula, we can calculate the number of words:
Total number of words = 26^6
= 26 * 26 * 26 * 26 * 26 * 26
= 26^6
= 308,915,776
Therefore, there are 308,915,776 words of length 8 that begin and end with the letter T.