Question

A license plate is identified by a string of three letters followed by two numbers. If each license plate is distinct, find the number of possible license plates.
1,123,200
1,757,600
1,404,000
1,423,656

Answer 1

The number of permutations of three letters taken 2 at a time is\[\frac{26!}{(26-3)!}\]
There are\[\frac{10!}{(10-2)!}=10\times 9=90\]permutations of 10 numbers taken 2 at a time.
The number of possible licence plates is\[26\times 25\times24\times 90\]