in how many ways can clean and clouded days occur in a week assuming that an entire day is either clean orclouded.
Any given day will be either clean or clouded, but not both. This means that for one single day, we have two choices- 1. Clean, 2. Clouded.
So number of choices for one day= 2 (or 2^1)
Number of choices for n days= 2^n (2 choices for every day)
Number of choices for 7 days= 1 week = 2^7 which is equal to the number of ways