I haven't figured out a or b, but here is the answer to part c:
1. Find the number of license plates with exactly four A's:
Choose 4 positions out of 6 for the A's: 6C4 = 15 ways
Fill the remaining 2 positions with any of the 26 letters: 26 * 26 = 676 ways
Total: 15 * 676 = 10,140 ways
2. Find the number of license plates with exactly two B's:
Choose 2 positions out of 6 for the B's: 6C2 = 15 ways
Fill the remaining 4 positions with any of the 26 letters: 26 * 26 * 26 * 26 = 456,976 ways
Total: 15 * 456,976 = 6,854,640 ways
3. Find the number of license plates with both four A's and two B's:
Choose 4 positions for the A's: 6C4 = 15 ways
Choose 2 of the remaining 2 positions for the B's: 2C2 = 1 way
Fill the remaining 0 positions: 1 way
Total: 15 * 1 * 1 = 15 ways
4. Find the total number of license plates:
Total = (Number with 4 A's) + (Number with 2 B's) - (Number with both)
Total = 10,140 + 6,854,640 - 15
Total = 6,864,765 ways
Therefore, there are 6,864,765 possible Aopslandian license plates that contain exactly four A's, or exactly two B's, or both.
