Exam 7: Sets and Counting

If $n ( A ) = 60$ , $n ( B ) = 24$ , and $n ( A \cap B ) = 3$ , find $n ( A \cup B )$ .

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of four of a kind (all four of one denomination and one of another). ​

In a study of the incidence of rickets in Tibetan children, a total of 1,551 urban and nonurban children were examined. Of these 1,012 had rickets. Of the 245 urban children in the study, 87 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. __________ children in nonurban areas had rickets ​ b. __________ children in nonurban areas did not have rickets

Let ​ B=\{ small, medium, large \} F=\{ oblong square \} ​ Represent the elements of $B \times F$ as cells in a spreadsheet. ​ $F\\B \left[ \begin{array} { l l } --&--- & \\--&--- & \\--&--- & \\\end{array} \right]$

How many ordered lists are there of 4 items chosen from 6 ?

Let $A = \{ \text { Dirk, Johan, Frans, Janet } \}$ , $B = \{ \text { Frans, Janet, Johan, Klass, Henrika } \}$ , $C = \{ \text { Dirk, Frans } \}$ . Find $n ( A \cup ( B \cap C ) )$ .

Use the given information to complete the solution of the partially solved Venn diagram. ​ $n ( A ) = 19$ , $n ( B ) = 16$ , $n ( C ) = 25$ , $n ( A \cap C ) = 9$ , and $n ( S ) = 59$ ​ ​ ​ $n ( k ) =$ __________ ​ $n ( q ) =$ __________ ​ $n ( m ) =$ __________ ​ $n ( r ) =$ __________ ​ $n ( p ) =$ __________

In an eight-cylinder engine, the even-numbered cylinders are on the left and the odd-numbered cylinders are on the right. A good firing order is a sequence of the numbers 1 through 8 in which right and left sides alternate. a. How many possible good firing sequences are there ? __________ sequences b. How many good firing sequences are there that start with a cylinder on the left ? __________ sequences

Let ​ P=\{ small, medium , large \} D=\{ circle, square \} ​ List the elements of $P \times D$ as ordered pairs in a set notation.

A bag contains 5 red marbles, 4 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many possible sets of three marbles are there

Evaluate $C ( 8,3 )$ . ​ $C ( 8,3 )$ __________

The number of ordered lists of 5 different items, chosen 8 at a time is 56.

Let ​ A =\{ June, Jill, Sally, Lucy \} B =\{ Jill, Lucy, Jelly \} C =\{ Ruth, Jill, Lucy \} ​ Find the set $( A \cup B ) \cup C$ . ​ $( A \cup B ) \cup C =$ __________

Let A =\{ Janet, Jill, Sally, Lucy \} B =\{ Jill, Lucy, Jennifer \} C =\{ Joan, Jill, Lucy \} Find the set $( A \cup B ) \cup C$ .

Let A =\{ Janet, Jill, Sally, Jolly \} B =\{ Jill, Jolly, Jennifer \} C =\{ Joan, Jill, Jolly \} Find the set $C \cap B$ .

Use a Venn diagram or some other method to obtain a formula for $n ( L \cup M \cup N )$ in terms of $n ( L )$ n $( M )$ $n ( N )$ $n ( L \cap M )$ $n ( L \cap N )$ $n ( M \cap N )$ , and $n ( L \cap M \cap N )$

You would like to see either a World War II movie or one that is based on a cartoon book character but does not feature robots. Which set of movies are you interested in seeing

An experiment requires a sequence of three steps. The first step can result in 6 possible outcomes, the second in 3 possible outcomes, and the third in 5 possible outcomes. What is the total number of outcomes possible ?

Evaluate $P ( 8,5 )$ .

Let ​ B =\{ blue , green \} G =\{ circle , square \} ​ List the elements of $B \times G$ as ordered pairs in a set notation.