Answer:
(a) 10,648,000
(b) 118,778,440
(c) 32,768
(d) 129,448,560
Explanation:
We use the counting principle.
(a)
22 × 22 × 22 × 10 × 10 × 10 = 10,648,000
(b)
3 letters: 22 × 22 × 22 = 10,648
4 letters: 22 × 22 × 22 × 22 = 234,256
5 letters: 22 × 22 × 22 × 22 × 22 = 5,153,632
6 letters: 22 × 22 × 22 × 22 × 22 × 22 = 113,379,904
Total:
10,648 + 234,256 + 5,153,632 + 113,379,904 = 118,778,440
(c)
32 × 32 × 32 = 32,768
(d)
This is the sum of the numbers of plates obtained in parts (a), (b), and (c), but we must make sure we do not count certain plates twice.
The 3-letter vanity plates are included in the vanity plates, so they have to be subtracted from the total number..
10,648,000 + 118,778,440 + 32,768 - 10,648 = 129,448,560