Full sail math self evaluation answers

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).