1. **Problem statement:** We want to find the number of different license plates possible with 4 letters followed by 2 digits. 2. **Total possible license plates:** Each of the 4 letters can be any of the 26 letters, and each of the 2 digits can be any of the 10 digits. Formula: $$\text{Total} = 26^4 \times 10^2$$ 3. **License plates with no repeated letters and no repeated digits:** - For letters: choose 4 different letters from 26 without repetition, order matters, so use permutations: $$P(26,4) = \frac{26!}{(26-4)!} = 26 \times 25 \times 24 \times 23$$ - For digits: choose 2 different digits from 10 without repetition, order matters: $$P(10,2) = \frac{10!}{(10-2)!} = 10 \times 9$$ 4. **Calculate total with no repetition:** $$P(26,4) \times P(10,2) = (26 \times 25 \times 24 \times 23) \times (10 \times 9)$$ 5. **Final answers:** - Total license plates: $$26^4 \times 10^2 = 456976 \times 100 = 45697600$$ - License plates with no repeated letters or digits: $$26 \times 25 \times 24 \times 23 \times 10 \times 9 = 35880000$$