Question

The layout for European license plates is XXX – XXXX. The first three digits are letters and the last four are numbers. The exclusions on the plates are that the first three letters cannot be the same (i.e. AAA) and the last four cannot be the same (i.e. 1111). How many different possible plates can be made? Show all work and explanations necessary.

Answer 1

No. of Plates Possible = 78624000 = 7.86 x 10⁷

Explanation:

We have total 7 places to fill in order to form a plate. So, we see all the number of options available for each of the position:

No. of Options for First Place = 26 (All alphabets of English)

No. of Options for Second Place = 25 (Due to no repetition)

No. of Options for Third Place = 24 (Due to no repetition)

No. of Options for Fourth Place = 10 (Digits from 0 to 9)

No. of Options for Fifth Place = 9 (Due to no repetition)

No. of Options for Sixth Place = 8 (Due to no repetition)

No. of Options for Seventh Place = 7 (Due to no repetition)

Hence, the total possible plates that can be made are given by multiplying

the options to select in each place:

No. of Plates Possible = 26*25*24*10*9*8*7

No. of Plates Possible = 78624000 = 7.86 x 10⁷