Subject identification numbers in a certain scientific research project consist of two letters followed by three digits and then two more letters. Assume repetitions are not allowed within any of the three groups, but letters in the first group of two may occur also in the last group of two. How many distinct identification numbers are possible? There are distinct identification numbers possible.

Step 1 ：The problem is asking for the number of distinct identification numbers possible. The identification number consists of two letters followed by three digits and then two more letters. Repetitions are not allowed within any of the three groups, but letters in the first group of two may occur also in the last group of two.

Step 2 ：To solve this problem, we need to calculate the number of possible combinations for each group and then multiply them together.

Step 3 ：For the first group of two letters, there are 26 possibilities for the first letter and 25 for the second (since repetitions are not allowed within the group). So, the total number of possibilities for the first group of letters is \(26 \times 25 = 650\).

Step 4 ：For the group of three digits, there are 10 possibilities (0-9) for the first digit, 9 for the second, and 8 for the third (since repetitions are not allowed within the group). So, the total number of possibilities for the digits is \(10 \times 9 \times 8 = 720\).

Step 5 ：For the last group of two letters, there are again 26 possibilities for the first letter and 25 for the second (since repetitions are not allowed within the group, but letters in the first group of two may occur also in the last group of two). So, the total number of possibilities for the second group of letters is \(26 \times 25 = 650\).

Step 6 ：Finally, to find the total number of distinct identification numbers possible, we multiply the number of possibilities for each group together. So, the total number of possibilities is \(650 \times 720 \times 650 = 304200000\).

Step 7 ：Final Answer: There are \(\boxed{304200000}\) distinct identification numbers possible.