4: In how many ways can five indistinguishable rooks be placed on an 8-by-8 chessboard so that no rook can attack another and neither the first row nor the first column is empty?

Q: In how many ways can a party of 5 persons arrange themselves in a row of 5 chairs?

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Q: How many ways are there to arrange 12 identical apples and five different oranges in a row so that…

A: Here, arrange 12 identical apples and five different oranges in a row so that no two oranges will…

Q: If a dealer randomly picks 5 cards from a standard deck that consists of 52 playing cards and then…

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Q: How many ways are there to place two identical queens on an 8 × 8 chessboard s so that the queens…

A: Solution:First let us find the number of ways where two two identical queens are on the same row or…

Q: 4. On Feb 25, 2021, there were 461,058 new cases of COVID reported in the world, 77803 in the US,…

A: Solution: Compared to the US, Oregon had 0.66% of the cases, but 0.41% of the deaths and 1.30% of…

Q: a. Seven people are standing in a row. How many ways can they permute themselves so that at most two…

A: (a) Here we see that, there are 7 persons in a row.  The number of ways they can be arranged among…

Q: A supermarket compiled the following information regarding 30 of its employees. 8 worked in the…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Your bowl contains 7 red balls, and 5 blue balls, and you draw 4 balls. In how many ways can the…

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Q: How many ways can you choose 3 pieces from the 4 kings and queens (black king, white king, black…

A: Permutation and Combination: A permutation is characterized as several aspects of putting some or…

Q: Suppose that we have a shipment of 50 microprocessors of which four are defective. In how many ways…

A: Given: shipment of 50 microprocessors of which four are defectiveTo find that:  In how many ways can…

Q: 11. Three standard six-sided dice, a blue, a red, and a yellow, are rolled, giving a sum of 13. The…

A: It is given that 3 dice are rolled which would have different colours, blue, red, and yellow. Assume…

Q: In how many ways can the television director of Exer-cise 38 fill the six time slots for commercials…

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Q: At a computer store, a customer is considering 6 different computers, 7 different monitors, 8…

A: Given that there are 6 different computers, 7 different monitors, 8 different printers, 4 different…

Q: 1| A shipment of 14 television sets includes three that are defective. In how many ways can a hotel…

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Q: If you roll to fair dice (one black die and one white die), in how many ways can you obtain a 6 on…

A: # If you roll to fair dice (one black die and one white die), in how many ways can you obtain a 6 on…

Q: (a) How many ways are there to distribute seven identical apples and six identical pears to three…

A: Given: To distribute seven distinct apples and six distinct pears.

Q: A clothing store has a certain shirt in four sizes: small, medium, large, and extra-large. If it has…

A: Given: The number of small-sized shirts is 3. The number of medium-sized shirts is 4. The number of…

Q: 1. The class Council is selling T-shirts that come in 3 colors ( yellow, blue, white) and 4 sizes…

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

Q: Suppose a certain combination lock requires three selections of numbers, each from 1 through 20 and…

A: 1 to 20 there are 20 numbers. Given that no number may be used twice. Means the combination will not…

Q: What is the main difference between a situation in which the use of the permutations rule is…

A: The major and main difference in the use of permutation rule and the combination rule is ordering.…

Q: Find the number m of ways that a class X with ten students can be partitioned into four teams A1,…

A:

Q: Suppose George loses 28% of all chess games. What is the probablity he loses 6 games in a row but…

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Q: How many different eleven-member football teams can be formed from a possible 35 players if…

A: Total no. of possible players = 35 No. of players in a team=11

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: Consider a system of two rolled dice, each having six possible states available to it (six different…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4. A computer center acquires eight different models of laptops of the same color and shape. If they…

A: We have in all 8 laptops in a drawer and choose 5 from them.

Q: Hello. How do I set up and work out this problem?

A: Given information:The total number of balls is 8.The number of black balls is 4 and the number of…

Q: How many Hokey teams of 6 players can be formed from 14 players without regard to position played?

A: Given ,no.of hokey players =14

Q: In how many ways can we distribute 10 indistinguishable oranges and 1 tangerine among 3 children…

A:

Q: suppose we color the squares of a 4×4 grid blue or red.Using inclusion-exclusion, how many ways can…

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Q: An urn contains 8 red balls, 3 green balls, and 1 white ball. Three are drawn simultaneously. Answer…

A: Given information: Number of red balls, r = 8 Number of green balls, g = 3 Number of white balls, w…

Q: A clothing store has a certain shirt in 4 sizes: small, medium, large, and extra-large. If it has 2…

A: Given Information -  The clothing store has shirts in 4 sizes: small, medium, large, and…

Q: A2. a. A company decided to distribute 5 identical computers among its employees. In how many…

A: The number of identical computers is 5. The number of distinct people is 3. Since, each employee…

Q: A certain cooperative has 15 men and 8 women. In how many ways can a committee of 6 members be…

A: GivenNo. of men =15no.of women = 8

Q: Suppose there are two prns, each filled with 100 balls. Um A contains 50 Blue balls and 50 Green…

A: Given :There are two urns, each filled with 100 balls. Urn A containts 50 Blue balls and 50 Green…

Q: Your bowl contains 6 red balls, and 7 blue balls, and you draw 4 balls. In how many ways can the…

A: Given: Bowl contains 6 red balls, and 7 blue balls. We have to draw 4 balls. The number of ways in…

Q: In how many ways can nine students be partitioned into three teams containing four, three, and two…

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Q: The Mars company offers customers the opportunity to create their own color mix of M&M’s candy.…

A: It can be calculated by using combination formula  C(n,r)=n! /(n−r)!(r)!

Q: andomly selected from a

A: we have given a sample of 6 measurements was randomly selected from normally distributed population…

Q: Suppose there are 14 freshman, 13 sophomores, 15 juniors, and 17 seniors running for the offices of…

A: There are 14 freshman, 13 sophomores, 15 juniors and 17 seniors.

Q: Rework problem 11 in section 2.3 of your textbook about selecting three (3) coins, but assume that…

A: Given information: The number of dimes is 5. The number of nickels is 4. The number of quarters is…

Q: How many distinct ways can we put kings on a 9 x 9 chessboard such that there are exactly 2 kings…

A: On a traditional 8 x 8 chessboard, there are only 2 ways to place 16 kings so that there are only 2…

Q: 2.25 A certain brand of shoes comes in 5 different styles, with each style available in 4 distinct…

A: Consider the data related to the shoe brand, styles, m=5colors, n=4 Each style with a color is a…

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

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Q: A firm is considering expanding into 5 of 14 possible cities. How many different groups of 5 cities…

A: The combination formula is nCx = n! /(n-x)! x!

Q: In the 1990s, significant numbers of tourists traveled from North America and Asia to Australia and…

A: Given that, Number of people visited Australia  n( Australia) = 2,231,000 Number of people visited…

Q: many permutations can be formed with two types of objects with n objects of type 1 and n^2 objects…

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Q: is the process of selecting from among a group of theoretically possible alternatives of those…

A: Denoting  is the process of selecting from among of theoretically possible alternatives of those…

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: 3. Find the number of distinct regular tetrahedral dice that can be made by coloring its faces with…

A: Given a tetrahedron... We should find the number of ways ...so that it can be painted....

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

A: