Examining License Plate Numbers
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Automobile license plate numbers are created using letters and digits.  State governments decide upon the specific arrangement of letters and numbers that will be used for each state.  It is important to choose wisely on the pattern of possible numbers and letters, since the possible number of combinations will determine the number of cars that can be registered at any one time.

1.  Complete the chart below showing how many combinations are possible (that is, how many cars can be registered) based upon the license plate arrangement schemes developed by each state.

State License Arrangement Scheme Number of Registered Cars
1 6 characters in the plate with three letters followed by three numbers  
2 6 characters in the plate with three letters (not the letter O) followed by three numbers OR three numbers followed by three letters (not the letter O).  
3 5 characters in the plate being either a letter or a number.  
4 4 characters in the plate being only letters.  
5 4 characters in the plate with one letter followed by 3 numbers.  

 

2.  A witness observes a motorist leaving the scene of a crime in State #1 (appearing in the chart above).  The witness remembers that the first three letters of the license plate on the get-away car were the letters UGG.  How many license numbers in this state start with these three letters?

 

3.  The city in which the crime discussed in question 2 occurred, represents approximately 5% of the state's total population.  How many cars from this city would fit the get-away car's description?

 

4.  Upon further reflection, the witness remembers that the car was a convertible with the top up.  If the state records show that only 12% of the state's registered cars are convertibles, how many state wide cars are suspect?  How many city cars are suspect?

 

5.  In State #3 (appearing in the chart above), a driver wants his license plate to begin with the letters BOB.  How many combinations are possible that start with BOB?

 

6.  In State #5 (appearing in the chart above), a driver wants her license plate to end with the her house number, 374.  How many combinations are possible that end with 374?