Thus, the probability of a water shortage in exactly two of the three months is:
**Thus, the probability of
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- Thus, the number of valid assignments is:
- The number of ways to choose 2 months out of 3 to have shortages is given by the binomial coefficient:
- The probability of shortages in exactly 2 months and no shortage in the remaining month is:
- An anthropologist is studying communication patterns in a group of 5 individuals, each of whom can choose to send a message using one of 4 different methods. How many distinct communication patterns exist if at least one individual must use each method?
- We need to count the number of ways to assign one of 4 methods to each of 5 individuals such that each method is used at least once.
- This is a problem of counting surjective (onto) functions from a set of 5 individuals to a set of 4 methods.
