Form an 8 letter word using A,B,C,D,E, if the letters in the word must appear in alphabetical order Form an 8 letter word using A,B,C,D,E, where each letter can be used multiple times. How many words can I form if the letters in the word must appear in alphabetical order?
For example: AABBDDDE is acceptable, BBBACCCE is not acceptable.
The only way I can think of to count this is to draw a table with the number of occurrences of each letter, then calculate the permutations of the letter positions for each row.
Is there an easier way to solve this question?

Observe that the type of word that you want is univocally decided by the numbers of letters A,B,C,D and E. Then the problem is the same of ask in how many ways can you write 8 as sum of 5 numbers, and the answer is ${12\choose 8}$, do you know why?
