suppose we color the squares of a 4×4 grid blue or red.Using inclusion-exclusion, how many ways can we color it so that no row has only one color

Q: A game is made up of triangular tiles that are equilateral with a number from the set {0,1,2,3,4,5}…

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Q: Find the number of ways of placing 12 balls in a row given that 5 are red, 3 are green and 4 are…

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Q: Compute how many different ways there are to color the faces of a cube so that three faces are red,…

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Q: Find the greatest common divisor (GCD) and the least common multiple (LCM) of 1575 and 66. Hence…

A: Given number's 1575 & 66  Division algorithm: If m and n are integers and n is positive there…

Q: A positive integer is divisible by 5, but it leaves remainders of 1 and 7 (resp.) when divided by 3…

A: Here we will use Chinese Remainder Theorem to find solution.

Q: A positive integer is divisible by 6, but it leaves remainders of 4 and 5 (resp.) Q.3. when divided…

A: Solution: Since the positive integer is divisible by 6, so suppose the required positive integer is…

Q: Faces of a polyhedron are painted into two colors, so that no two faces sharing an edge have the…

A: Consider the provided question, We need to prove that the number of edges of all faces of polyhedron…

Q: Determine the number of ways in which the four corners of a squarecan be colored with two colors.

A: Number of corners of square 1, 2, 3, 4 in counterclockwise direction as in picture

Q: 2) For a balanced incomplete block design, suppose you have 8 treatments and know that there can…

A: Given :-For a balanced incomplete block design, suppose you have 8 treatments and know that there…

Q: Suppose we have L-shaped tiles made up of three squares: Prove that for all n > 1, it's possible to…

A: Suppose we have L shaped tiles Prove that for all n>=1 it's possible to lay these tiles down to…

Q: A garderning company is planting trees and flowers at 3 sites on the median of a new road. For each…

A: * SOLUTION :-

Q: Prove that a 6x6 board cannot be tiled with the tile shown. Use the coloring of the board to justify…

A: According to the given information, it is required to prove that 6×6 board cannot be tiled with the…

Q: Find the norm of the partitionP = {−5,−4.3,−3.2,−2.3,−1.8,−1}

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Q: A rectanglular table seats 6 people; I person on each end and 2 on each of the longer sides. Thus,…

A: Six people can sit in a rectangular table with two people on the shorter side and four people on the…

Q: 5. Assume that each scoop can only hold a maximum of 8 pieces and a minimum of 2. How many ways are…

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Q: Suppose that a coach must select 5 players to play on a basketball team. • The coach has 13 players…

A: The coach has 13 player to select from  And only 4 players can play center, so one of them has to be…

Q: What is the conjugate of the partition (n – k) + k, where n 2 2 and n = isks \n/2]?

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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: Define Row addition ?

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Q: • Suppose that a coach must select 5 players to play on a basketball team. • The coach has 12…

A: Given that there are 3 players who can play center. So we can choose center in 3 ways only.  When…

Q: When I arrange the members of a marching band in rows of 2, 3, or 4, there is always 1 person left…

A: To solve the given problem

Q: How many Lettuce paths from a to b avoiding the blue squares

A: Let us consider a 2*2 box for example. It is part of the big square.   Let say the present location…

Q: If a system produces a true statement by the elimination method, it has no solution. True O False o…

A: Question : If a. System produces true statement by the elimination method.it has no solution . True…

Q: If six black, five red, four white, and two green disks are to be arranged in a row, what is the…

A: Permutation: the permutation is determining the number of possible arrangements in a set when the…

Q: Cells B1, C1, and D1 contain the values Seat1Row1, Seat1Row2, and Seat1Row3. Of cells B1,C1, and D1…

A: Given, Cells B1, C1, and D1 contain the values Seat1Row1, Seat1Row2, and Seat1Row3. Of cells B1,C1,…

Q: If we take a golden rectangle which has base equal to φ and height equal to 1, and we subdivide that…

A: Given: Height and base of rectangle are 1 unit and φ unit.   To find: Dimension of smaller rectangle…

Q: A triangular system may be an echelon system but an echelon system may not be triangular. True False

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Q: Determine the number of ways in which the edges of a square can becolored with six colors so that no…

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Q: A positive integer is divisible by 6, but it leaves remainders of 4 and 5 (resp.) when divided by 5…

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Q: snip

A: It is given that, in a food court there are four locations available for four vendors and food court…

Q: In row 2 there are 28 seats and in row 4 there are 44 seats. What is the number of seats in row 10?

A: The given data in the question is converted into a table

Q: Suppose we live in Z², namely the 2D grid of integers. We start at (0,0) and want to reach (6, 8).…

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Q: 1.) How many sides does a polygon have if the maximum number of diagonals that you can draw inside…

A: ( As per Bartleby guidelines we are supposed to answer only one question at a time from a given…

Q: What are the two things we need to show in order to prove that (S,*) is a mathematical system?

A: Please see the below detailed solution.

Q: The Japanese game called Chu Shogi uses a square board. The board is covered with smaller squares…

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Q: A certain kind of a ceramic tile has the form of a 4 × 4 board. Each of the 16 squares is colored…

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Q: If a block is drawn from the box as shown above 200 times with replacement, predict the number of…

A: Given : Box :

Q: 4. If I have a group of x soldiers, and I divide them into rows to learn the remainder of x when…

A: Let us determine whether the statement is TRUE or FALSE in the next step.

Q: The board of directors of a cooperation must select a president, a secretary, and a treasurer. In…

A: Total members on the board of directors = 15 members

Q: Suppose two squares of the same color are removed from an 8 x 8 chessboard. Is it possible to tile…

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Q: Each of the 20 students learn exactly two of the three languages: English, French and German. 80% of…

A: Total number of students= 20 Number of students learn English= 80% of 20 = (80÷100)*20= 16 Number of…

Q: be run under the building. If these two blocks must always be next to each other, how many s can the…

A: Given Here we have 7 blocks ,but we  have to keep 2 perticular blocks together. So we have to…

Q: How many ways can you arrange 8 identical towers on a chessboard so that no two are standing…

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Q: How many polygons can be possibly made from 6 distinct points on a plane, no three of which are…

A: Answer: 42 polygons can be possibly made from 6 distinct points on a plane, no three of which are…

Q: Two steps of the Gauss-Jordan elimination method are shown. Fill in the missing numbers.

A: Given,            11-1944512505  →11-10-5?0-4?5??

Q: Find a sequence of row operations carryıng b, + a h, + 2 b, + e, C; + az a, + b a, + b, a, + b, az h…

A: Question: Find a sequence of row operations carrying b1+c1b2+c2b3+c3c1+a1c2+a2c3+a3a1+b1a2+b2a3+b3…

Q: In how many ways can six indistinguishable rooks be placed on an 8x8 chessboard so that no rook can…

A: there are (nCk)(nCk) ways of choosing a subset of k x k rows. there are k!k! ways of ordering the…

Q: two diagonally opposite corners of a standard chessboard are removed. Is it possible to cover the…

A: Given that, Two diagonally opposite corners of a standard chessboard are removed. Every domino in a…

Q: Show that a 6 × n board (n ≥ 2) can be tiled with L-shaped tiles, without gap and overlapping. Each…

A: Before we begin proving the statement, we shall understand the shapes. An L-shaped three-square tile…

Q: At the beginning of a game of chess, the back row consists of two (identical) rooks on the corners,…

A: