Suppose that in a particular Finite course, 5/14 of students plan on majoring in math, 11/42 plan on majoring in history, and 1/7 plan on double majoring in math and history. How many want to major in exactly one of history or math?

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A: Given, A fleet of 9 taxis is to dispatch to the three airports A, B, and C also, 2 go to A, 6 go to…

Q: Suppose that there are nine students in a discrete mathematics class at a small college a) show that…

A: Given: 9 students in a discrete mathematics

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A: Given:- total books =10 maths books =4 Chemistry books =3 history books =2 song lyric book =1

Q: If positive integers are chosen at random, what is the minimum number you must have in order to…

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Q: There are five distinct computer science books, three distinct mathe- matics books, and two distinct…

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Q: Suppose that every student in a discrete mathematics class of 31 students is a freshman, a…

A: Given that, every student in a discrete mathematics class of 31 students is a freshman, a sophomore,…

Q: Suppose that 11 children collected 50 books. Prove by contradiction that at least two of them had…

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Q: A box contains 15 balls in which seven are green and eight are yellow. If five balls must be drawn…

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Q: uppose the sap is collected in gallon buckets that hang under each tap, and that the maple syrup…

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Q: How many four-digit passwords can be made from the digits 0 to 5, if digits can be repeated?

A: From 0 to 5 there are 6 digits.  Given that the digits can be repeated. This means for each digit…

Q: A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second day, he…

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Q: In a certain get together, there was a basket of fruits for every three guests, a basket of cookies…

A: Let the number of fruit baskets be x, the number of cookies baskets  be y and the number of chips…

Q: Each student in a 40-person Finite Mathematics class was asked which homework system(s) they would…

A: The shaded region in the following Venn diagram represents the set, A∪B∪C .

Q: 2. A group contains k men and k women, where k is a positive integer. How many ways are there to…

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Q: Show that among any 4 n−1 people, there are either some n of them who mutually know each other, or…

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Q: Suppose that in a particular class of 135 students, 45 of them are majoring in math, 60 of them are…

A: Let, A be the students who are major in math, B be the students who are major in communications.…

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: When the repetition is allowed in formation the general formula for calculating the possibility is…

Q: How many strings of three decimal digits

A: Strings of three decimal digits:

Q: A committee of 5 consisting of 3 girls and 2 boys is to be chosen from a class with 15 girls and 10…

A: Given: Total Number of Girls=15Total Number of Boys=10Commitee required 5 candidate in whichNumber…

Q: Select the following statements that are true. The number of bit strings of length n that start with…

A: Option b,c and e are True

Q: Suppose in a small town named Oshiland there are three places to eat, a Chinese restaurant, a…

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Q: A certain committee consists of 7 people. From the committee, a president, a vice president, a…

A: Solution: We need to choose a committe of a president , a vice president, a , a secretary, and a…

Q: Show that if 2n−1 is prime then n is prime.

A: We have to show that if 2n-1 is prime then n is prime.

Q: How many 5-digit numbers can be made from the digits 1 to 9 if: a) Repetition of digits is allowed?…

A: Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART ONLY

Q: 2. Prove that if m and n are integers and mn is even, then m is even or n is even.

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Q: A certain committee consists of 20 people. From the committee, a president, a vice-president, a…

A: Given : A certain committee consists of 20 people Now we have to choose a president, a…

Q: Suppose 34% of students chose to study German their junior year, and that meant that there were 272…

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Q: 2. Suppose that a password for a computer system must have at least 8, but no more than 12,…

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Q: a town of 3,000 people, 600 are over 50 years of age and 400 are left-handed. It is also known that…

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Q: If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which…

A: The number of r combinations which can be selected from n numbers if repetitions allowed is…

Q: a lock has a code of 3 numbers between 1 and 20. if no numbers in the code are allowed to repeat,…

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Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: There are 6 positions in the license plate that need to be filled. Out of these 6, first 4 positions…

Q: How many landline telephone numbers are there with 7 digits such that: (c) the two initial digits…

A: Given: Number of digits in a telephone number = 7 Total number of digits = 10 (0 to 9) Number of odd…

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

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Q: Suppose that in a particular Finite course, 4/7 of students plan on majoring in math, 25/42 plan on…

A: Given that, in a particular finite course, 47 of students plans majoring in math, 2542 plans…

Q: 3) Among a group of seven (not necessarily consecutive) integers, how many must be divided by 5 to…

A: This is a problem related to divination rule of the mathematics. Based on the general concept we…

Q: 1. How many combinations are there to pick r objects from 2n objects numbered from 1 to 2n with n >…

A: For the solution of the problem follow the next step.

Q: Suppose that in a particular Finite course, 4/7 of student plan on majoring in math, 25/42 plan on…

A: Given Information- 4/7 of student plan on majoring in Math, 25/42 plan on majoring in…

Q: Suppose that every student in a discrete mathematics class of 25 students is a freshman, a…

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Q: Since the next prime after 7 is​ 11, the smallest composite number whose prime factors are all…

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Q: Suppose that 150 people celebrated their birthday in three months, where 65 people celebrated their…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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Q: Question 1 Each student in a 40-person Finite Mathematics class was asked which homework system(s)…

A: Given that, H= student who were satisfied with handwritten homework . O= students who were satisfied…

Q: If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which…

A: As we know that any truples h,i,j,k,m with n≥h≥i≥j≥k≥m≥1  can be represented as a string of n-1…

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

A: Given, Each license plate in a certain state has one digit followed by four letters followed by one…

Q: 2. Show directly that sup(4) = 1 for A = {1- : n eN}.

A: As we know that, 1>1-1n ∀ n∈ℕ Therefore 1 is the upper bound of the set 1-1n:n∈ℕ. And for each…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.