1. The problem asks how many 5-letter words can be formed using the letters A, B, C, D, E where letter A appears exactly 3 times. 2. Since the word length is 5, and A occurs exactly 3 times, we choose which 3 positions out of 5 are occupied by A. The number of ways to choose positions is $$\binom{5}{3} = 10.$$ 3. The remaining 2 positions can be filled by any of the other 4 letters (B, C, D, E). 4. Each of these 2 positions can be chosen independently from 4 letters, so total ways to fill these 2 positions is $$4^2 = 16.$$ 5. Therefore, the total number of words is $$10 \times 16 = 160.$$ **Final answer:** 160