A three-digit code for certain locks uses

A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

1 Explanation

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Jeffrey Braganza

3 digit Code: X Y Z

If Y is 0:
X – cannot have 0 or 1, so we can have 2 to 9 inclusive, 8 possible numbers
Y – 0, so 1 possible no
Z – if Y is 0, Z cannot be 0, so Z can be 1 to 9 inclusive, 9 possible nos

If Y is 1:
X – cannot have 0 or 1, so we can have 2 to 9 inclusive, 8 possible numbers
Y – 1, so 1 possible no
Z – if Y is 1, Z can be 0 to 9 inclusive, 10 possible nos

(8*1*9) + (8*1*10) = 72 + 80 = 152

Jan 17, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Great job! Thanks for posting your solution :)

Jan 19, 2016 • Reply