In how many ways can 8 people be lined up so that: (a) persons A, B, C occupy the first, second and third places in the row respectively b) persons A and B stand next to each other, and two other persons stand between them and person C (c) persons A and B were not standing next to each other

Q: On Monday, Tom worked 2 hours and Sylvester worked 3 hours and they made a total of 23 mouse traps.…

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Q: N-1 1 R(N) = - - N2 R(i) i=1 Hint: R(N) is the probability of the event. How can you break it down…

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Q: A family with three children are to pose for a family picture in a row. la) In how ways can they be…

A: Given Information: A family with three children are to pose for a family picture in a row.  (a) In…

Q: Suppose we want to choose 4 objects, without replacement, from 18 distinct objects. (a) How many…

A: Permutations and combinations

Q: s) I am creating a seating chart for my class with 15 students. The front row has 7 seats and Ashley…

A: Here total tudents = n =15 Front row has 7 seats and ashley and blake must be sit next to each…

Q: 7. Six chairs are equally spaced around a circular table. What is the number of ways that three men…

A: See this solution in below.

Q: n how many ways can 5 men, 4 women, and 3 children be arranged in a row of 12 seats if a. the men…

A: Given that  Number of men = 5 Number of women = 4 Number of children = 3 Number of seats in the row…

Q: n how many different ways can you seat 11 men and 8 women in a row? b) In how many different ways…

A: We know that, combination is an arrangement of items in which order does not matter. A permutation…

Q: may a. In how many ways may the scholarships be awarded such that 2 men and 2 women are selected. b.…

A: Here given , there are 4 different prizes  And here there are 5 men and 4 women in group of scholar…

Q: A homeowner doing some remodeling requires the services of both a plumbing contractorand an…

A: Given: There are 12 plumbing contractors and 9 electrical contractors available in the area. As 1…

Q: Three couples, the Smiths, Joneses, and Murphys, are going to form a line. (a) In how many such…

A: The number of ways to arrange n items is calculated using the formula n!. For the arrangements in…

Q: In how many ways can we seat 6 boys and 3 girls on a row of seats so that no two girls sit next to…

A: If no two girls can sit together, then we need to alternate boy and girl. We can start with a boy…

Q: b. A machinist produces 22 items during a shift. Three of the 22 items are defective and the rest…

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Q: If A+B=X and A-B=Y then...?

A: System of linear equations,

Q: On Monday, tom worked 2 hours and Sylvester worked 3 hours and they made a total of 23 traps. On…

A: Let 'x' be the number of traps Tom does 'y' be the number of traps Sylvester does 'z' be the number…

Q: Mr. Arboreta wants to plant fruit trees in a rectangular array. For each of the following numbers…

A: A number of objects or elements arranged in a row and Column is called a rectangular Array. In that…

Q: I have a bucket of n green balls labeled 1, 2, . . . , n. I have another bucket of red balls labeled…

A: The events are occurring simultaneously. So,  Total combinations=combinations for green…