Sequential Counting Principle ( SCP)

Question

A witness observes a motorist leaving the scene of a crime in state 1. The witness remembers that the first three letters of the license plate on the get-away car were the letters RED. How many license numbers in this state start with these three letters?

 

State 1: 6 character in the plate with three letters followed by three numbers. Number of registered cares 17,576,00.

Answer 1

"three letters followed by three numbers"   and   "first three letters ...  were the letters RED"

 

 So,

    RED000

    RED001

    RED002

    RED003

    RED004

     . . .

    RED999

 

That is 1000 plates because decimal is a positional number system.

 

Note that State 1 is in serious trouble if 17, 576,000 cars are registered, because:

     26*26*26*10*10*10 = 17,576,000

   All possible license plates have been assigned, including:

       OOO000

       III111

       SSS555

         [and various other undesirable combinations]