2015 NYJC P2 Q11

A briefcase is fitted with two combination locks, one each for the left and right clasps. Each lock consists of \(3\) rotary digital counters. To unlock each lock, the correct combination of \(3\) digits (\(0\) to \(9\)) must be dialled. Find the total number of possible combinations that can be set for the \(2\) locks if

1. there are no restrictions,[1]
2. the code for the left lock must have \(3\) identical digits and the code for the right lock must have \(3\) identical digits but different from that for the left lock,[2]
3. the access codes have digits that are all different and include the digits of the owner’s birth year which is \(1970\),[3]
4. no digit for the code for the left lock can be used for the code for the right lock.[4]