A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 according to the ...
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 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?
Answer/Solution
119
Steps/Work
The first digit can be filled in 7 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 10 values
number of codes = 7 * 1 * 9 = 63
Case 2 -
If second digit is 0,Third digit can take 8 values ( Third digit can't be zero)
number of codes = 7 * 1 * 8= 56
Total number of codes = 119
Answer A
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 10 values
number of codes = 7 * 1 * 9 = 63
Case 2 -
If second digit is 0,Third digit can take 8 values ( Third digit can't be zero)
number of codes = 7 * 1 * 8= 56
Total number of codes = 119
Answer A