Exam 7: Sets and Counting

A surgical procedure requires four steps. The first step can result in 3 possible outcomes, the second in 5 possible outcomes, and the remaining two can each result in 4 possible outcomes. What is the total number of outcomes possible ?

If $n ( A \cup B ) = 140$ and $n ( A ) = n ( B ) = 75$ , find $n ( A \cap B )$ . ​ $n ( A \cap B ) =$ __________

Find the indicated value. ​ 7!

Evaluate $C ( 3,1 )$ . ​ $C ( 3,1 ) =$ __________

If $n ( A ) = 90$ , $n ( A \cup B ) = 190$ , and $n ( A \cap B ) = 30$ , find $n ( B )$ . ​ $n ( B ) =$ __________

How many possible calendars are there that have February 15 falling on a Monday, or Tuesday ? __________ calendars

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). ​

How many five-letter sequences are possible that use the letters b, l, a, c, k once each

In how many ways can a 6-card hand containing 4 kings and 2 queens be dealt from a deck of 36 cards

Evaluate $C ( 7,4 )$ .

List the elements of all outcomes of rolling two indistinguishable dice such that the numbers add up to 8. ​ The answer is __________.

A telephone number consists of a sequence of seven digits not starting with a 0 or a 1. How many phone numbers begin with either 764, 768, or 788

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. How many possible good firing sequences are there ?

A test requires that you answer first Part A and then either Part B or Part C. Part A consists of 6 true/false questions, Part B consists of 9 multiple choice questions with one correct answer out of 5, and Part C requires you to match 8 questions with 8 different answers. (Each question matches exactly one correct answer.) How many different completed answer sheets are possible ? __________ sheets

Let N =\{ small, medium, large \} A =\{ hexagon, triangle \} List the elements of $N \times A$ as ordered pairs in a set notation.

Evaluate $P ( 6,2 )$ . ​ $P ( 6,2 )$ __________

The following table shows the amount spent, in billions of dollars, on recreational boats and accessories in the United States during the period 1999-2001. (Let S be the set of all dollars represented in the table.) Compute the cardinality of the set described as $n ( N \cap C )$ . Used Boats, New Boats, Accessories, Total , 5 6 3 14 , 9 9.5 4 22.5 , 9 6 4 19 Total 23 21.5 11 55.5 ​ ​ $n ( N \cap C ) =$ __________ billion dollars.

Use the given information to complete the solution to the partially solved Venn diagram. $n ( A ) = 24$ , $n ( B ) = 19$ , $n ( C ) = 30$ , $n ( A \cap C ) = 6$ , and $n ( S ) = 51$

Let $S = \{ \text { Bamsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows, Witbank Aces, Royal Tigers, Dundee United, Lyon } \}$ be a universal set, $A = \{ \text { Dundee United, Witbank Aces, Maroka Swallows, Royal Tigers } \}$ , and $B = \{ \text { Sheffield United, Manchester United, Dundee United } \}$ . Find $n \left( ( A \cup B ) ^ { \prime } \right)$ .

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 1 lavender marble. How many possible sets of three marbles are ther