Exam 7: Sets and Counting

Find the indicated value. ​7! ​

Let A =\{ June, Jill, Molly, Jolly \} B =\{ Jill, Jolly, Jennifer \} C =\{ Rachel, Jill, Jolly \} Find the set $A \cap ( B \cap C )$ .

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 3 lavender marbles. How many sets of 4 marbles include at most one of the yellow marbles

Let ​ A=\{ June, Jeffrey, Solly, Polly \} B=\{ Jeffrey, Polly, Jennifer \} C=\{ Ruth, Jeffrey, Polly \} ​ Find the set $A \cap ( B \cap C )$ . ​ $A \cap ( B \cap C ) =$ __________

The following table shows the results of a survey of authors by a fictitious publishing company. New Authors Established Authors Total Successful 2 25 27 Unsuccessful 14 56 70 Total 16 81 97 Consider the following subsets of the set S of all authors represented in the table: C, the set of successful authors; U, the set of unsuccessful authors; N, the set of new authors; and E, the set of established authors. Find the number of elements that set contains. Use the table to compute $n ( C \cup N )$ .

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A). ​ __________ hands

The World Almanac features a "perpetual calendar", a collection of possible calendars for every conceivable year. Find the lowest number of the calendars. ​

Evaluate $P ( 7,5 )$ .

Of the 5,700 students at medium Suburban College, 50 play collegiate soccer, 60 play collegiate lacrosse, and 80 play collegiate football. Only 4 play both collegiate soccer and lacrosse, 6 play collegiate soccer and football, and 15 play collegiate lacrosse and football. No students play all three sports. ​ Complete the following sentence: ______% of the college soccer players also play one of the other two sports at the collegiate level. ​

A freelance computer consultant keeps a database of her clients, which contains the names ? $S = \{ \text { Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert } \}$ ? The following clients owe her money. ? $N = \{ \text { Acme, Floyd, Effigy, Global } \}$ ? The following clients have employed her in the last year. ? $P = \{ \text { Acme, Floyd, Dion, Effigy, Global, Hilbert } \}$ ? Write the clients who do not owe her money or have employed her in the last year. ? The answer is __________

Let ​ A=\{ Jello, Jeffrey, Solly, Lucy \} B=\{ Jeffrey, Lucy, Jelly \} C=\{ Joan, Jeffrey, Lucy \} ​ Find the set $A \cup ( B \cup C )$ .

In a study of the incidence of rickets in Tibetan children, a total of 1,556 urban and nonurban children were examined. Of these 1,019 had rickets. Of the 235 urban children in the study, 90 had rickets. Use Venn diagrams to determine how many children in nonurban areas had rickets, and how many children in nonurban areas did not have rickets.

A computer byte consists of 8 bits, each bit being either a 0 or a 1. If characters are represented using a code that uses 2 bytes for each character, how many characters can be represented ?

List the set of all outcomes of tossing three indistinguishable coins.