1. **Problem statement:** Vasya forms 5-letter words using the letters A, B, C, D, E. These words must have exactly one A and exactly two Bs. The remaining two letters can be any of the letters C, D, or E. 2. **Determine the number of ways to arrange the letters:** - Since the word length is 5, and we have 1 A and 2 Bs fixed exactly, - That means 2 remaining letters can be any from {C, D, E} allowing repeats. 3. **Step 1: Choose positions for A and Bs** - Number of ways to select 1 position for A out of 5: $$\binom{5}{1} = 5$$ - Number of ways to choose 2 positions for Bs out of remaining 4: $$\binom{4}{2} = 6$$ - Total ways to position A and Bs: $$5 \times 6 = 30$$ 4. **Step 2: Choose letters for the remaining 2 positions** - Each position can be any of C, D, or E (3 choices each) - Number of ways: $$3^2 = 9$$ 5. **Step 3: Total number of words** - Multiply the position arrangements by letter choices: $$30 \times 9 = 270$$ **Final answer:** There are 270 such words Vasya can write.