The problem is to find the number of elements in the sample space.
We have four patients and 4 categories of diseases.
Event A: All patients are in the same category
Event B: 2 patients belong to the same category
My question is why is the answer here $4^4$.
As far as I see it:
for one category (S...same category, D...different category):
A = {SSSS}
B ={SSDD, DSSD, DDSS, SDDS, SDSD, DSDS}
So why cant we just multiply 7 times 4 categories and get a sample space of 20?