5 A security code consists of 2 letters followed by a 4-digit number. The letters are chosen from \(\{ \mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } \}\) and the digits are chosen from \(\{ 1,2,3,4,5,6,7 \}\). No letter or digit may appear more than once. An example of a code is BE 3216 .

1. How many different codes can be formed?
2. Find the number of different codes that include the letter A or the digit 5 or both.
   A security code is formed at random.
3. Find the probability that the code is DE followed by a number between 4500 and 5000 .