Bunuel wrote:

A 9-character numeric passcode is constructed at random. If the last number cannot be prime and the first digit cannot be 0, 1, or 7, how many different codes can be constructed?

A. 210,000,000

B. 300,000,000

C. 360,000,000

D. 420,000,000

E. 560,000,000

The first digit excludes [0, 1 and 7] , therefore 7 possible values.

The last digit excludes [2, 3, 5 and 7] therefore 6 possible values

The second to eight digits (7 digits) can have all 10 values

Therefore different codes that can be constructed is 7*10*10*10*10*10*10*10*6 = 7*6*(10^7) = 420,000,000

Hence

option D = 420,000,000 is the answer.

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