91Ó°ÊÓ

Let \(A=\\{\) June, Janet, Jill, Justin, Jeffrey, Jello\\}, \(B=\\{\) Janet, Jello, Justin\\}, and \(C=\\{\) Sally, Solly, Molly, Jolly, Jello\\}. Find each set. $$ (A \cap B) \cap C $$

A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. How many sets of three marbles include none of the yellow ones?

If a die is rolled 30 times, there are \(6^{30}\) different sequences possible.Ask how many of these sequences satisfy certain conditions. What fraction of these sequences have exactly five 1 s?

If a die is rolled 30 times, there are \(6^{30}\) different sequences possible.Ask how many of these sequences satisfy certain conditions. What fraction of these sequences have exactly 15 even numbers?

Let \(S\) be the set of outcomes when two distinguishable dice are rolled, let \(E\) be the subset of outcomes in which at least one die shows an even number, and let \(F\) be the subset of outcomes in which at least one die shows an odd number. List the elements in each subset given. $$ F^{\prime} $$

License Plates \(^{12}\) License plates in Montana have a sequence consisting of: (1) a digit from 1 to \(9,(2)\) a letter, \((3)\) a dot, (4) a letter, and (5) a four-digit number. a. How many different license plates are possible? b. How many different license plates are available for citizens if numbers that end with 0 are reserved for official state vehicles?

Use Venn diagrams to illustrate the following identities for subsets \(A, B\), and \(\operatorname{Cof} S .\) $$ \begin{aligned} &(A \cap B) \cap C=A \cap(B \cap C)\\\ &\text { Associative Law } \end{aligned} $$

Use Venn diagrams to illustrate the following identities for subsets \(A, B\), and \(\operatorname{Cof} S .\) $$ A \cup(B \cap C)=(A \cup B) \cap(A \cup C) \quad \text { Distributive Law } $$

Use Venn diagrams to illustrate the following identities for subsets \(A, B\), and \(\operatorname{Cof} S .\) $$ A \cap(B \cup C)=(A \cap B) \cup(A \cap C) \quad \text { Distributive Law } $$

Use Venn diagrams to illustrate the following identities for subsets \(A, B\), and \(\operatorname{Cof} S .\) $$ S^{\prime}=\emptyset $$