A student is allowed to select at most n books from a collection of (2n+1) books. If the total number of ways in whtch he can select a book ts 63. Find the yalue of n.

Q: Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to…

A: Three married couples are to be seated in a row having six seats in a cinema hall. We have three…

Q: A number is called “quadary” if each digit is either 0, 1, 2, or 3. How many different 5-digit…

A: Given that a number quadary if each digit is either 0,1,2 or 3. To find the number of  different…

Q: . Bricks are stacked in 20 rows such that each row has a fixed number of bricks more than the row…

A:

Q: 1. In a segment of 207.5 fm, Forever Radio. Dj Lam-ang can play 5 love songs in a row. If there are…

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

A: It is given that the integers are from 1 through n, and no number appear more than 3 times.

Q: If a men working 6hours a day can do a work in 88days, then 6men working 8hours a day can do it in…

A: Given that men working 6 hours a day can do work in 88 days

Q: Prove that the sum of any three consecutive numbers is divisible by 3

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

A: * License plate must have       3 letters and 3 digits ; repetitions allowed.Also , letters H and L…

Q: A large amphitheater is set up in such a way that there are 16 seats in the first row 27 seats in…

A: The given problem is regarding arithmetic progression series. First-term is given. A common…

Q: A supermarket send codes for $0.25 off a bag of chips to its rewards members. Each coupon code will…

A: Number of letters allowed = 24 Number of digits allowed = 7 Each coupon code will have one digit…

Q: ay be formed using the digits 2, 3, 4, 6 and 9 if repetitions

A: 22,23,24,26,29,32,33,34,36,39,42,43,44,46,49,62,63,64,66,69,92,93,94,96,99. In unit digit place we…

Q: f n ∈ n and n<2000 , how many numbers n have the property that the sum of the digits of n and the…

A: Given, if n∈ℕ and  n&lt;2000.

Q: Suppose you must use 1x“-tile and 10 x-tiles. You only have up to 15 1-til use. How many of the…

A: Introduction: A rectangle is a quadrilateral with equal angles and opposite sides that are equal and…

Q: When all n teams in a league play every other team twice, a total of N games are played, N=n2 - n. A…

A: Given, total number of games played, N=n2 - n Number of team, n = 6

Q: How many total ways can we form a 3-letter password or a 4-letter password using the letters from…

A:

Q: For a segment of a radio show, a disc jockey can play 5 records. If there are 9 records to select…

A:

Q: A group of 9 people consisting of 4 mothers and 5 children bought tickets for the cinema in the same…

A: A group of 9 people consisting of 4 mothers and 5 children bought tickets for the cinema in the same…

Q: How many committees are possible if the committee must have a least two men?

A: Concept:   The number of ways of achieving success that is the total number of possible outcomes is…

Q: If there are 10 people and only 6 chairs are available, in how many ways can they be seated?

A: 1st person can choose any of the 10 seats. 2nd person can choose any of the 9 seats now available…

Q: In a stack of cards, each card has a number and letter on opposite sides. You are told that all…

A: Each card has a number and a letter on opposite sides. Any number that is even as well as divisible…

Q: mball machine dispenses 5 varieties of gumball (red, blue, green, yellow, and pink). How many…

A: a. The collections of 10 gumballs, at least 6 of which are red are ,  The cases obtained are  6 red…

Q: Find in how many ways can two admirals, three generals, and four lieutenants can be seated in a row…

A: Total seats = 9 Admirals =2 Generals=3 Lieutenants =4

Q: The number of distinct arrangements of all the letters in the word BAMBOO is

A: Here we use the formula The number of distinct arrangements of all the letters is =((total number of…

Q: Three married couples have purchased tickets for a play. Spouses are to be seated next to each…

A: Given :  Three married couples purchased tickets.                 To find  :  How…

Q: A committee has 10 members and 4 members must be chosen for a subcommittee. Three of the 10 members…

A: Statisticians/mathematicians use different counting techniques while selecting or arranging members…

Q: Suppose a n × n chessboard is missing two opposite corners. Prove that no matter what n is, you will…

A:

Q: In a large math conference with 2022 participants, each person shakes hands with some number of…

A: For 'n' number of participants the maximum number of handshakes is n(n-1)/2.

Q: Spider has one sock and one shoe for each of its 8 legs. In how many different ways can the spider…

A: There are 8 socks and 8 shoes.

Q: The digits 1, 2, 3 and 4 can be arranged to form different four-digit codes. a. Find the number of…

A:

Q: Suppose that 6 machines can complete a certain task in 9 days. If there are 18 machines, how many…

A: Concept: If number of machine increase then number of work completion day will decrease . Hence Both…

Q: Two integers, a and b, have a product of 48. What is the least possible sum of a and b? The least…

A: Answer is a+b= -49. Explanation is given below...

Q: In how many ways can this be done if at least two of the committee members must be senator?

A:

Q: Find an integer that leaves a remainder of 2 whan divided by either 3 or 5, but that is divisible by…

A:

Q: A supermarket wants to send codes for $0.25 off a bag of chips to its rewards program members. Each…

A: Given, a supermarket wants to send codes for $0.25 off a bag at chips to its rewards program…

Q: 4. Find the sum of positive divisor of 5,020 and also find the pair of this number so that they can…

A: We have to find the sum of all divisor of 5020 and then the amicable pair of the number.

Q: If n∈N and n<2000 , how many numbers n have the property that the sum of the digits of n and the sum…

A:

Q: 10 identical copies of a movie will be stored on 40 computers such that each computer has at most 1…

A: Given the statement. 10 identical copies of a movie will be stored on 40 computers such that each…

Q: Find the number of arrangements of the digits {0,1,2,3,4,5,6,7,8,9} such that the first digit is…

A: We need to find the total number of arrangements of digits 0,1,2,3,4,5,6,7,8,9 such that the first…

Q: in 2  rows  there are  5 armchairs  and all are  occupied , in how many  differnt  ways can theses…

A: Given: Number of Rows =2. Number of armchair = 5. To determine the number of ways substitute the…

Q: select three (3) coins, but assume that there are 5 dimes, 4 nickels, and 2 quarters. In how many…

A:

Q: How many distinct integers do we have to pick in order to have two that have the same remainder when…

A: To find - How many distinct integers do we have to pick in order to have two that have the same…

Q: Can you think of the smallest number N such that ot can be expressed as a product of the two factors…

A: We have to find out the number N that can be expressed as a product of the two factors which are…

Q: Six COVID patient arrived in a hospital. Unfortunately, there are only 2 vacant beds. In How many…

A: According to given data there are only 2 vacant beds and six Covid patient arrived in hospital So,…

Q: bookshelf has space for exactly 12 books. In how many ways can the books be arranged on the…

A:

Q: A restaurant offers a dinner special that lets you choose from 10 entrees, 8 side dishes, and 13…

A: Multiplication rule of counting:If a task consists of a sequence of choices in which there are ‘a’…

Q: A sheet of paper is cut into 2 same size parts. Each of the parts is then cut into 2 same- size…

A: Let's figure out how it goes with the number of cuts: Number of cuts pieces of paper…

Q: Red and blue ceramic tiles are laid according to a pattern such that for every 22 red tiles used, 3…

A: Given that there are total 300 ties of Red and blue colour .according to pattern every 22 red…

Q: How many ways are there to pick five people for a committee if there are six (different) men and…

A:

Q: Find the least natural number a with the property that the sum a + 2ā + 3a + ...+ 9a is the number…

A:

Q: What 2 nonnegative numbers with a sum of 23 have the largest possible product?

A: Given information: The two non negative numbers with a sum of 23.  Calculation: Consider x and y are…