Lets suppose we are solving a clustering problem over data sample 2 in Table 3 with 3 binary attribute 1, attribute 2 and attribute 3. How many distinct instances we can get? What if we add 7 more binary attributes attribute 4, attribute 5, ..., attribute 10, how many distinct instances can we get? Elaborate what the potential problem is when adding more attributes to the data sample and propose your solution (with details) to solve this problem.

Table 3 Data Sample 2 Instance Attribute 1 1 Y 2 N 3 Y Attribute 2 N Y N Attribute 3 Y N N