Math 10B Quiz 3-
1. (a) Fill in the blanks: The Stirling number S(n, k) counts the number of ways to ________________ (arbitrarily/surjectively/injectively) put n _______________________ (distinguishable/indistinguishable) balls into k ____________________ (distinguishable/indistinguishable) boxes.
(b) Compute S(7, 5). (It's a three digit number.)
2. In a class, there are 30 students taking a quiz. Each quiz score will be an integer between -10 and 10 inclusive. How many different quiz score distributions are possible for the class? Here, a quiz score distribution records only the number of -10 scores, the number of -9 scores, . . . , the number of 10 scores.
3. A weather forecaster says:
- There is a 0.6 probability it will rain in Berkeley today.
- There is a 0.4 probability it will rain in Berkeley tomorrow.
- There is a 0.1 probability it will rain in Berkeley both today and tomorrow.
Assuming mathematical consistency of the weather forecaster's statements, what is the probability there is no rain in Berkeley today nor tomorrow?