Full Sail Discrete Mathematics Answers

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Need both tests within 48 hours, thanks. Test 7 earlier if possible.

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LMS | Student Portal 2/20/17, 2(15 PM (/) 7.1 | Fundamentals : Combinatorics Test in WEEK 4-1 : COUNTING AND EFFICIENCY 1 " 22 ! FEB STATUS There are 17 Game Development majors and 15 Software Development majors in a class. In how many ways can one representative be chosen who is either a Game Development major or a Software Development major? 10 Points 17 15 32 255 2 There are 17 Game Development majors and 15 Software Development majors in a class. In how many ways can two representatives be chosen such that one is a Game Development major and the other is a Software Development major? 10 Points 15 17 32 255 3 How many bit strings are there of length 3? 10 Points 2 4 8 16 https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 1 of 10 LMS | Student Portal 4 2/20/17, 2(15 PM How many bit strings of length 8 are there? 10 Points 8 255 256 128 5 How many strings of four letters are there? Repetition is permitted. Consider lower case only. 10 Points 26 + 26 + 26 + 26 26 × 4 26 × 26 × 26 × 26 26 × 25 × 24 × 23 6 How many strings of four letters do not have the letter "x"? Repetition is permitted. Consider lower case only. 10 Points 26 × 26 × 26 × 26 − 1 25 × 25 × 25 × 25 25 + 25 + 25 + 25 26 × 26 × 26 × 26 − 4 7 How many strings of four letters have the letter "x" in them? Repetition is permitted. Consider lower case only. 10 Points 25 ⋅ 24 ⋅ 23 26 ⋅ 25 ⋅ 24 ⋅ 23 https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 2 of 10 LMS | Student Portal 2/20/17, 2(15 PM 264 264 − 254 8 Suppose you are creating a game with two factions, seven races, two genders, eleven classes, and three specializations. To create a character you choose a faction, race, gender, class, and specialization. How many unique characters can be created under this scheme? 10 Points 25 924 308 462 9 The inclusion exclusion principle states that given two sets, A and B , the cardinality of A by |A ∪ B| = |A| + |B| − |A ∩ B| . If |A| ∪ B is given = 10, |B| = 8 , and |A ∩ B| = 5, then what is the cardinality of A ∪ B? 10 Points |A ∪ B| = 10 |A ∪ B| = 18 |A ∪ B| = 13 |A ∪ B| = 7 10 Suppose every student in our class can write C++ or Java. Suppose there are 18 students that can write C++, 23 students that can write Java, and 7 students that can write both C++ and Java. How many students are in our class? 10 Points 11 16 41 34 https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 3 of 10 LMS | Student Portal 11 2/20/17, 2(15 PM What is the formula for the number of combinations of r elements from a set with n elements? 10 Points n! r! n! C(n, r) = n − r! C(n, r) = 12 C(n, r) = n! (n − r)! C(n, r) = n! (n − r)!r! What is the formula for the number of permutations of r elements from a set with n elements? 10 Points n! r! n! P(n, r) = n − r! P(n, r) = 13 P(n, r) = n! (n − r)! P(n, r) = n! (n − r)!r! How many ways are there to seat four of a group of ten people in a row? 10 Points 10! 4! 10! 10 − 4! 10! (10 − 4)! 10! (10 − 4)!4! 14 How many bit strings of length 12 contain exactly three 1s? 10 Points https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 4 of 10 LMS | Student Portal 2/20/17, 2(15 PM 1320 36 220 4096 15 How many bit strings of length 12 contain at most three 1s? 10 Points C( 12,12 ) - C( 12, 3 ) C( 12, 0 ) + C( 12, 1 ) + C( 12, 2 ) + C( 12, 3 ) P( 12, 0 ) + P( 12, 1 ) + P( 12, 2 ) + P( 12, 3 ) P( 12, 12 ) - P( 12, 3 ) 16 How many bit strings of length 12 have an equal number of 0s and 1s? 10 Points P( 12, 6 ) P( 12, 2 ) C( 12, 6 ) 2×2×2×2×2×2 17 How many permutations of the letters A, B, C, D, E, F, G, H contain the string DCE? 10 Points P( 8, 5 ) P( 6, 6 ) P( 8, 6 ) P( 8, 8 ) https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 5 of 10 LMS | Student Portal 18 2/20/17, 2(15 PM How many permutations of the letters A, B, C, D, E, F, G, H contain the strings BA and FGH? 10 Points P( 8, 3 ) P( 6, 6 ) P( 6, 3 ) P( 5, 5 ) 19 How many permutations of the letters A, B, C, D, E, F, G, H contain the strings BCA and ABF? 10 Points P( 4, 4 ) P( 3, 3 ) P( 1, 1 ) 0 20 Suppose a game has 7 diﬀerent character classes available to players. When designing large team raids, what is the smallest number of players needed to guarantee that there will be 3 players of the same character class? 10 Points 10 15 21 21 Use the binomial theorem to ﬁnd the coeﬃcient of x 5 y8 in (x + y)13 . 10 Points P( 13, 8 ) C( 13, 8 ) P( 13, 5 ) C( 8, 5 ) https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 6 of 10 LMS | Student Portal 22 2/20/17, 2(15 PM Given a standard deck of cards, how many ﬁve card hands can be made? 10 Points 52! 5! 52! 52 − 5! 52! (52 − 5)! 52! (52 − 5)!5! 23 Consider the grid below. Paths can go up or right (not left and not down). How many paths are there from (0,0) to (5,3)? Hint: the directions can be translated into binary since there are only 2 options for movement 10 Points 8 15 56 125 336 6720 24 https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 7 of 10 LMS | Student Portal 2/20/17, 2(15 PM When rolling a pair of 10-sided dice What is the probability that the sum of the two results is less than 5? Note: the values on a 10 sided die are 0 through 9 (there is not a 10) 10 Points 0.05 0.1 0.12 0.15 0 : It is not possible 25 When rolling a 10 sided die What is the probability that the result will be prime and even? Note: the values on a 10 sided die are 0 through 9 (there is not a 10) 10 Points 0 0.1 0.4 0.5 0.8 0.9 26 When rolling a 10 sided die What is the probability that the result will be prime or odd? Note: the values on a 10 sided die are 0 through 9 (there is not a 10) https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 8 of 10 LMS | Student Portal 2/20/17, 2(15 PM 10 Points 0 0.1 0.4 0.6 0.7 0.9 27 What is the probability that you will be dealt a 5 card hand that contains no Face Cards? (Face cards are Jack, Queen, or King) 10 Points 0 : It is impossible 0.125 about 0.253 about 0.747 0.875 28 When rolling a 10 sided die What is the probability that the result will be less than 6? Note: the values on a 10 sided die are 0 through 9 (there is not a 10) 0 Points 0.4 0.5 0.6 0.7 29 What is the size of the sample space for the following scenario: Roll 3 six-sided dice, and add up the two smallest values (do not use the highest roll) https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 9 of 10 LMS | Student Portal 2/20/17, 2(15 PM 10 Points 11 12 36 216 30 Which of the following is more likely? 1. Rolling a pair of six sided dice and getting a sum of less than 10 2. Rolling 3 six sided dice, discarding the highest result, and getting a sum of less than 8 10 Points 1. The scenario where you roll 2 dice is more likely 2. The scenario where you roll 3 dice and discard the highest is more likely Submit Comments https://course.fso.fullsail.edu/class_sections/68473/exams/1735568 Page 10 of 10 LMS | Student Portal 2/20/17, 2(16 PM (/) 8.1 | Fundamentals : Efficiency of Algorithms Test in WEEK 4-1 : COUNTING AND EFFICIENCY 1 " 25 ! FEB STATUS What does computational complexity measure? 5 Points The time needed to complete an algorithm (measured in number of steps) The amount of memory (records that need to be checked or references) The type of mathematical operations required (integration is more complex that addition) 2 Which of these functions grows the most slowly? (A big O of this would indicate the most eﬃcient algorithm) 5 Points f (n) = n log n f (n) = n f (n) = 1 f (n) = log n 3 Which of these functions grows the most slowly? (A big O of this would indicate the most eﬃcient algorithm ) 5 Points f (n) = n f (n) = 2n f (n) = n2 f (n) = n log n https://course.fso.fullsail.edu/class_sections/68473/exams/1735558 Page 1 of 7 LMS | Student Portal 4 2/20/17, 2(16 PM Which of these functions grows the most slowly? (A big O of this would indicate the most eﬃcient algorithm ) 5 Points f (n) = n f (n) = n log n f (n) = n2 f (n) = log n 5 Which of these functions grows the most slowly? (A big O of this would indicate the most eﬃcient algorithm ) 5 Points f (n) = n! f (n) = 2n f (n) = log n f (n) = n 6 Which of these functions grows the most quickly? (A big O of this would indicate the least eﬃcient algorithm ) 5 Points f (n) = log n f (n) = n! f (n) = 2n f (n) = n2 7 Which of these functions grows the most quickly? (A big O of this would indicate the least eﬃcient algorithm ) 5 Points https://course.fso.fullsail.edu/class_sections/68473/exams/1735558 Page 2 of 7 LMS | Student Portal 2/20/17, 2(16 PM f (n) = n log n f (n) = 2n f (n) = log n f (n) = n2 8 Which of these functions grows the most quickly? (A big O of this would indicate the least eﬃcient algorithm ) 5 Points f (n) = n f (n) = n log n f (n) = 1 f (n) = log n 9 Which of these functions grows the most quickly? (A big O of this would indicate the least eﬃcient algorithm ) 5 Points f (n) = n log n f (n) = n2 f (n) = n f (n) = 2n 10 The Towers of Hanoi (http://vornlocher.de/tower.html) game/puzzle is a visual example of a type of recursive algorithm. Visit the site and try to move the towers of diﬀerent sizes and watch the example solution for the large number of discs. What is the minimum number of steps would it take to transfer a tower of 9 discs from Tower 1 to Tower 3? 5 Points 362880 Steps 59049 Steps 511 Steps https://course.fso.fullsail.edu/class_sections/68473/exams/1735558 Page 3 of 7 LMS | Student Portal 2/20/17, 2(16 PM 81 Steps 11 What is the estimated Big-O complexity for solving a Tower of Hanoi Problem of size n ? (That is, moving a tower with n discs from Tower 1 to Tower 3) 5 Points O(1) : Constant Time Complexity O(log n) : Logarithmic Time Complexity O(n) : Linear Time Complexity O(n ⋅ log n) : "Linearithmic" Time complexity O(n3 ) : Polynomial Time Complexity O(2n ) : Exponential Time Complexity O(n!) : Factorial Time Complexity 12 The Guess the Number game is essentially a search for an unknown number. You can also try your strategy using a web app available here (http://www.mathcats.com/explore/puzzles/guessmynumber.html) How many guesses would you need to determine the number out of 1 through 100 in worst case using a linear search? Note: The questions are about the method (algorithm) used for ﬁnding the number, not the veriﬁcation process the game does. 5 Points 100 guesses 50 guesses 13 guesses 7 guesses 6 guesses 13 The Guess the Number game is essentially a search for an unknown number. https://course.fso.fullsail.edu/class_sections/68473/exams/1735558 Page 4 of 7 LMS | Student Portal 2/20/17, 2(16 PM You can also try your strategy using a web app available here (http://www.mathcats.com/explore/puzzles/guessmynumber.html) How many guesses would you need to determine the number out of 1 through 100 in worst case using a binary search? Note: The questions are about the method (algorithm) used for ﬁnding the number, not the veriﬁcation process the game does. 5 Points 100 guesses 50 guesses 13 guesses 7 guesses 6 guesses 14 What is the Big-O complexity of a Linear Search? 5 Points O(1) : Constant Time Complexity O(log n) : Logarithmic Time Complexity O(n) : Linear Time Complexity O(n ⋅ log n) : "Linearithmic" Time complexity O(n2 ) : Polynomial Time Complexity O(2n ) : Exponential Time Complexity 15 What is the estimated Big-O complexity for a Binary Search? 5 Points O(1) : Constant Time Complexity O(log n) : Logarithmic Time Complexity O(n) : Linear Time Complexity O(n2 ) : Polynomial Time Complexity O(n!) : Factorial Time Complexity https://course.fso.fullsail.edu/class_sections/68473/exams/1735558 Page 5 of 7 LMS | Student Portal 16 2/20/17, 2(16 PM Suppose that an element is known to be among the ﬁrst four elements in a list of 64 elements. Would a linear search or a binary search locate this element more rapidly? 5 Points Linear Search Binary Search 17 Suppose we do not have information about where in the list of 64 elements an element appears. Would a linear search or a binary search locate this element more rapidly? 5 Points Linear Search Binary Search 18 What is the initial value for i in the for-loop below: For i = 1 to 7 Step 1 Step 2 ... End − f or 5 Points 0 1 19 Give a big-O estimate for the number of additions used in this segment of an algorithm. t:=0 for (i:=1;i
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Hi, below are the solutions to both assignments. The answers are marked in red dots.

LMS | Student Portal

2/20/17, 2(16 PM

(/)

8.1 | Fundamentals : Efficiency of Algorithms
Test in WEEK 4-1 : COUNTING AND EFFICIENCY

FEB

STATUS

What does computational complexity measure?
5 Points
The time needed to complete an algorithm (measured in number of steps)
The amount of memory (records that need to be checked or references)
The type of mathematical operations required (integration is more complex that addition)

Which of these functions grows the most slowly?
(A big O of this would indicate the most eﬃcient algorithm)
5 Points
f (n) = n log n
f (n) = n
f (n) = 1
f (n) = log n

Which of these functions grows the most slowly?
(A big O of this would indicate the most eﬃcient algorithm )
5 Points
f (n) = n
f (n) = 2n
f (n) = n2
f (n) = n log n

https://course.fso.fullsail.edu/class_sections/68473/exams/1735558

Page 1 of 7

LMS | Student Portal

2/20/17, 2(16 PM

Which of these functions grows the most slowly?
(A big O of this would indicate the most eﬃcient algorithm )
5...

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