Answer:
Explanation:
12 seconds to try one combination will be equivalent to 
Password contain at least 8 digit i.e. password can contain 8, 9, 10 digit.
Password cannot contain more than 10 digit because it will give room for repetition which it is clearly stated that digit cannot be repeated.
Possible digit that can be used: 9,8,7,6,5,4,3,2,1,0.
Total number of passwords combination possible for each position in 8 digit.
1st position = 10, 2nd position = 9, 3rd position = 8, 4th position = 7, 5th position = 6, 6th position = 5, 7th position = 4, 8th position = 3. Total number of passwords combination possible in 8 digit is equivalent to 
.
Total number of passwords combination possible for each position in 9 digit.
1st position = 10, 2nd position = 9, 3rd position = 8, 4th position = 7, 5th position = 6, 6th position = 5, 7th position = 4, 8th position = 3, 9th position = 2. Total number of passwords combination possible in 9 digit is equivalent to 
.
Total number of passwords combination possible for each position in 10 digit.
1st position = 10, 2nd position = 9, 3rd position = 8, 4th position = 7, 5th position = 6, 6th position = 5, 7th position = 4, 8th position = 3, 9th position = 2, 10th position = 1. Total number of passwords combination possible in 10 digit is equivalent to 10!.
Adding them up and multiplying by 
to get the total number of time needed to guarantee access to database = ![[\frac{10!}{2}\times\ \frac{10!}{1} \times 10!] \frac{1}{5}\ mins = \frac{10!}{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B10%21%7D%7B2%7D%5Ctimes%5C%20%5Cfrac%7B10%21%7D%7B1%7D%20%5Ctimes%2010%21%5D%20%5Cfrac%7B1%7D%7B5%7D%5C%20mins%20%3D%20%5Cfrac%7B10%21%7D%7B2%7D)
