Permutation and Combination Problem

[sukhman]

A password contains at least 8 distinct digits. It takes 12 seconds to try one combination, what is theminimum amount of time required to guarantee access to the database? (10P8 + 10P9 + 10P10) × 12 seconds

[ganeshrkamath]

A password contains at least 8 distinct digits. It takes 12 seconds to try one combination, what is theminimum amount of time required to guarantee access to the database? (10P8 + 10P9 + 10P10) × 12 seconds

For guaranteed access, we should use brute force method.
Choose and arrange 8 distinct digits out of 10 => 10P8
Choose and arrange 9 distinct digits out of 10 => 10P9
Choose and arrange 10 distinct digits out of 10 => 10P10

Total number of tries = 10P8 + 10P9 + 10P10
Since each trial takes 12 seconds, total time = (10P8 + 10P9 + 10P10) * 12 seconds

Cheers