Question

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

Answer 1

There are 5 places to fill

2 places of alphabet(out of 26) can be filled in $=26\ast 25ways$

3 places of digits(out of 10) can be filled in $=10\ast 9\ast 8ways$

No of different plates $=26\ast 25\ast 10\ast 9\ast 8=468000$