License plates in a particular state are to consist of 3 digits followed by 3 uppercase letters.
c) How many different license plates can there be in this state if the first and second digits must be even, and repetition of letters and numbers is not permitted?
d) How many different license plates can there be in this state if the first digit cannot be 7, and repetition of letters and numbers is not permitted?
+23246 c) There are 5 even digits (0, 2, 4, 6, 8)
First digit = 5 possibilities
Second digit = 4 possibilities
Third digit = 8 possibilities
First letter = 26 possibilities
Second letter = 25 possibilities
Third letter = 24 possibilities
Total number of possibilities = 5 x 4 x 8 x 26 x 25 x 24 = ...
d) First digit = 9 possibilities
Second digit = 9 possibilities
Third digit = 8 possibilities
First letter = 26 possibilities
Second letter = 25 possibilities
Third letter = 24 possibilities
Total number of possibilities = 9 x 9 x 8 x 26 x 25 x 24 = ...
