I found following Problem in Introductory Combinatorics text book:
How many eight-letter words can be constructed by using the 26 letters of the alphabet if each word contains three vowels? It is understood that there is no restriction on the number of times a letter can be used in a word
I tried to solve the problem in following manners:
There are 5C3 ways we can select 3 vowels from the alphabet and 21C5 ways to select 5 consonant from 21 consonants. For each such 8 characters selection we can arrange the word in $8^8$ ways (as repetition of character is allowed).
My answer: $5C3 \cdot 21C5 \cdot 8^8$
But textbook has the following answer: $8C5 \cdot 5^3 \cdot 21^5$
Could you please help me know where I am going wrong.