List the elements in the given set. The set of all outcomes of rolling two distinguishable dice such that the numbers add to 6
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How many different five-letter sequences can be formed from the letters a, a, a, b, c?
You are exhibiting your collection of minimalist paintings. Art critics have raved about your paintings, each of which consists of 10 vertical colored lines set against a white background. You have used the following rule to produce your paintings: Every second line, starting with the first, is to be either blue or gray, while the remaining five lines are to be either all light blue, all red, or all purple. Your collection is complete: Every possible combination that satisfies the rules occurs. How many paintings are you exhibiting?
Use Venn diagrams to illustrate the given identity for subsets \(A, B,\) and \(C\) of \(S\). \(A \cap(B \cup C)=(A \cap B) \cup(A \cap C) \quad\) Distributive law
The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. There are five appetizers, two soups, four main courses, and five desserts, Your diet restricts you to choosing between a dessert and an appetizer. (You cannot have both.) Given this restriction, how many three-course meals are possible?
A surgical procedure requires four steps. The first can result in four possible outcomes, the second can result in three possible outcomes, and the remaining two can each result in two possible outcomes. What is the total number of outcomes possible?
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