Probability

# Absolute Complement

Chef Connie Cookie prepared a meal that consisted of 5 different dishes. The dishes were supposed to be served to the customers in the order Appetizer, Soup, Salad, Entree, Dessert, however the waitstaff served them in the wrong order. How many different incorrect ways could the waitstaff have served the dishes?

Details and assumptions

A way is incorrect if at least one dish wasn't served in its intended place.

The city council of Springfield consists of $13$ male members and $10$ female members. How many ways are there to elect a president and vice president such that at least one of the two leaders is female?

A class of students takes a test of five true and false questions. If no student answers all questions correctly, no student answers all questions incorrectly, and no two students give the same sequence of answers, what is the maximum number of students in the class?

This problem is posed by Eeshan U.

The set $S$ has 6 elements. How many subsets of $S$ are there with two or more elements?

There are two sets $X= \{ a, b, c, d \}$ and $Y= \{ a, e, i, o, u \}$. How many of the functions whose domain is $X$ and codomain is $Y$, are not one-to-one?

Details and assumptions

You may choose to read up on Function Terminology.

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