Licence plates in Catalunya (Spain) are of the form ·XX consists of one or two l

Question

Licence plates in Catalunya (Spain) are of the form ·XX consists of one or two letters and identifies the Catalan province where the vehide is registered: B (Barcelona), (Tarragona) NNNIN is a sequence number consisting of tour digits (padded with teading zeroes i necessary, and consonants Q and R, and two-letter combinations ending in the vowels A E, I and O were also forbidden, apparently to eries consisting of first one and then two two letters which incremented after the sequence number reached 9999 1t never uses the offensive words For example, the order of licence plates for vehicles registered in Barcelona was B-0000-AB-0001-AB-0002 “A B-0000-BB-0001-B.B-0002-B, , B-9999-A B-9999-B B-0000-Z, B-0001-Z,B-0002-, B- 9999-Z B-0000-AA, B-0001-AA B-0002-AA,B-9999-AA 8-0000-AB B-0001-AB, B-0002-AB,B-9999-AB B-0000-ZZ, B-0001-ZZ, B-0002-ZZ, B-9999-Zz How many Catalan licence plates are possible? Number

Explanation / Answer

XX-NNNN-YY

XX can be filled only with B, GI, L or T so total ways = 4
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NNNN can be filled with any digits (0,1,2,3,4,5,6,7,9)
That is total 10 ways for each N
so NNNN can be filled in 10*10*10*10=10000 ways.

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YY can be "single letter" or "two letter"

case 1: YY is single letter
it can take any letter from A to z except Q and R
so that means 24 letters are available for this case.

case 2: YY is two letter

first letter can be any letter from A to z except Q and R
so that means 24 letters are available for first letter.

2nd letter can be any letter from A to z except Q and R and vovel (A,E,I,O,U)
so that means 19 letters are available for second letter.

so total such cases are 19*24=456

so YY can be filled in 24+456=480 ways.

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So total number of number plates as per given situation = 4*10000*480 =19200000
Hence final answer is 19200000

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