Download Discrete Math Test 2 Questions with complete solution 2026 and more Exams Mathematics in PDF only on Docsity!
Discrete Math Test 2 Questions with
complete solution 2026
a. 325×18 = 5850 b. 325+18 = 343 - correct answer ✔There are 18 mathematics majors and 325 computer science majors at a college. a. In how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? b. In how many ways can one representative be picked who is either a mathematics major or a computer science major? a. 4¹⁰ b. 5¹⁰ - correct answer ✔A multiple-choice test contains 10 questions. There are four possible answers for each question. a. In how many ways can a student answer the questions on the test if the student answers every question? b. In how many ways can a student answer the questions on the test if the student can leave answers blank? 7×6 = 42 - correct answer ✔Six different flights fly from New York to Denver and seven fly from Denver to San Francisco. How many different pairs of airlines can you choose on which to book a trip from New York to San Francisco via Denver, when you pick an airline for the flight to Denver and an airline for the continuation flight to San Francisco?
26³ - correct answer ✔How many different three-letter initials can people have? 26² = 676 - correct answer ✔How many different three-letter initials are there that begin with A? 2⁸ - correct answer ✔How many bit strings of length 10 both begin and end with 1? n - correct answer ✔How many bit strings with length not exceeding n, where n is a positive integer, consist entirely of 1s, not counting the empty string? 26+26²+26³+26⁴ = 475,254 - correct answer ✔How many strings are there of lowercase letters of length four or less, not counting the empty string? a. 10³-10 = 990 b. 5×10² = 500 c. 10+10+10-3 = 27 - correct answer ✔How many strings of three decimal digits a. do not contain the same digit three times? b. begin with an odd digit? c. have exactly 2 digits that are 4? 3⁵⁰ - correct answer ✔A committee is formed consisting of one representative from each of the 50 states in the United States, where the representative from a state is either the governor or one of the two senators from that state. How many ways are there to form this committee?
d. that start with a vowel, if letters cannot be repeated? e. that contain at least one vowel, if letters can be repeated? f. that contain exactly one vowel, if letters can be repeated? g. that start with X and contain at least one vowel, if letters can be repeated? h. that start and end with X and contain at least one vowel, if letters can be repeated? a. 2×5! = 240 b. 6!-(2×5!) = 480 c. 6!÷2 = 360 - correct answer ✔In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if a. the bride must be next to the groom? b. the bride is not next to the groom? c. the bride is positioned somewhere to the left of the groom? (2⁸+2⁷)-2⁵ = 352 - correct answer ✔How many bit strings of length 10 either begin with three 0s or end with two 0s? C(4,0)x⁴ + C(4,1)x³y + C(4,2)x²y² + C(4,3)xy³ + C(4,4)y⁴ = x⁴+4x³y+6x²y²+4xy³+y⁴ - correct answer ✔Find the expansion of (x+y)⁴ 101 - correct answer ✔How many terms are there in the expansion of (x+y)¹⁰⁰?
-2¹⁰×C(19,10) - correct answer ✔What is the coefficient of x⁹ in (2-x)¹⁹ {{abc}, {acb}, {bac}, {bca}, {cab}, {cba}} - correct answer ✔List all of the permutations of {abc} 6! = 720 - correct answer ✔How many permutations of {abcdefg} end with a? a. 5!/(5-1)! = 5 b. 6! = 720 c. 8!÷(8-1)! = 8 d. 8!÷(8-5)! = 6720 e. 8!÷(8-8)! = 40, f. 10!÷(10-9)! = 3,628,800 - correct answer ✔Find the value of each of these quantities a. P(5,1) b. P(6, 5) c. P(8, 1) d. P(8, 5) e. P(8, 8) f. P(10, 9)
a. 2¹⁰ = 1024 b. C(10,3) = 120 c. 2¹⁰ - [C(10,2)+C(10,1)+C(10,0)] = 968 d. C(10,5) = 252 - correct answer ✔A coin is flipped 10 times where each flip comes up either heads or tails. How many possible outcomes a. are there in total? b. contain exactly 3 heads? c. contain at least 3 heads? d. contain the same number of heads and tails? a. 7! = 5040 b. 6! = 720 c. 5! = 120 d. 5! = 120 e. 4! = 24 (CAB and BED both contain B therefore CABED must be a substring) f. 0 (impossible since BCA and ABF both contain B) - correct answer ✔How many permutations of the letters ABCDEFGH contain
a. the string ED? b. the string CDE? c. the strings BA and FGH? d. the strings AB, DE, GH? e. the strings CAB and BED? f. the strings BCA and ABF? 8!×C(9,5)×5! = 609,638,400 - correct answer ✔How many ways are there for 8 men and 5 women to stand in a line so that no two women stand next to each other? a. 100×99×98×97 = 94,109, b. 99×98×97 = 941, c. 4×(99×98×97) = 3,764, d. 99×98×97×96 = 90,345, e. 98×97×P(4,2) = 114, f. 97×P(4,3) = 2328 g. 4! = 24 h. 96×95×94×93 = 79,727,
a. 5×21⁵×C(6,1) = 122,523, 030 b. (5²×21⁴)×C(6,2) = 72,930, c. 26⁶-21⁶ = 223,149, d. 26⁶-21⁶-122,523,030 = 100,626,625 - correct answer ✔How many strings of 6 lowercase letters of the English alphabet contain a. exactly one vowel? b. exactly two vowels? c. at least one vowel? d. at least two vowels? C(15,3)×C(10,3) = 54,600 - correct answer ✔Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee with six members if it must have the same number of men and women? C(10,3)+C(10,4)+C(10,5)+C(10,6)+c(10,7) = 912 - correct answer ✔How many bit strings of length 10 contain at least 3 1s and at least 3 0s? 26×25×24×10×9×8 = 11,232,000 - correct answer ✔How many license plates consisting of three letters followed by three digits contain no letter or digit twice? 3⁵ = 243 - correct answer ✔In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed? 26⁶ = 308,915,776 - correct answer ✔How many strings of 6 letters are there?
5³ = 125 - correct answer ✔How many ways are there to assign three jobs to five employees if each employee can be given more than one job? C(7,3) = 35 (3 stars, 4 bars) - correct answer ✔How many ways are there to select three unordered elements from a set with five elements when repetition is allowed? a. C(13,6) = 1716 b. C(19,12) = 50, c. C(31,24) = 2,629, d. C(11,4) = 330 - correct answer ✔A bagel shop has onion, poppy, egg, salty, pumpernickel, sesame, raisin, and plain bagels. How many ways are there to choose a. 6 bagels? b. a dozen bagels? c. two dozen bagels? d. a dozen bagels with at least one of each kind? 9 Simply count: 0 pennies and 8 nickels 1 penny and 7 nickels 2 pennies and 6 nickels 3 pennies and 5 nickels
