A rooming house has three rooms that contains four beds, three beds and two beds respectively. In how many ways can nine quests be assigned to these rooms?

The book says it is 1260. I have no idea how they got this. I know it requires combinations. Could someone please explain it to me. Thanks a lot.

  1. 👍 0
  2. 👎 0
  3. 👁 1,067
  1. consider the rooms first.

    Room 1: 9*8*7*6 ways for guests to be there
    Room 2: 5*4*3 ways to be there
    room 1: 2 ways to be there.

    Now consider the beds: 4!3!2!=ways to arrange the beds in rooms.

    (multipy the first three, divide by the ways beds can be arraged.


    1. 👍 0
    2. 👎 0
  2. First Room- P(9,4)= 126 [9 people with 4 beds]
    Second Room- P(5,3)= 10 [since the first room has 4 beds, there are only 5 people left and this room contains 3 beds]
    Third Room- P (2,2)= 1 [7 out of the 9 people have already their own beds in room 1 and 2. Therefore, there are only 2 people left in the room that contains 2 beds.
    126*10*1= 1260

    1. 👍 2
    2. 👎 0
  3. Anonymous has the best response with regards to the Nelson Math of Data Management textbook which has this exact question relating to combinations. However, instead of P(9,4) x P(5,3) x P(2,2), it is actually C(9,4) x C(5,3) x C (2,2)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. English

    Choose incorrect if the sentence is punctuated incorrectly. Choose correct if it is punctuated correctly. 1: Gravel, crushed rock, cinder- these are used as ballast on railroad beds. Correct*** 2:Ben Franklin[noted statesmen,

  2. Statistics

    A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is cancelled before 6:00 PM deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use

  3. math

    if the pediatric floor of a hospital has 165 beds, how many rooms are there if each room hold 3 beds?

  4. math

    The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side of the playground. The length of the playground is l and its width is w. The length of

  1. English

    The day we found the sharks' teeth was foggy and cool. Moisture hung in the air so thick you could almost see it sparkling in the dim sunlight. There were days, early in the summer like this one, where it seemed there was more

  2. English

    Please help if I did right! Thanks. Whose brilliant idea was this anyway?" Sarah asked." If people were intended to sleep on the ground and cook over a fire, we wouldn't have beds and microwave ovens." "Stop complaining," Emily

  3. Englih rhymes

    Solutions to th rhymes below are made up of one possessive noun and one plural noun: spectacles for a young lady. tales of a boy named Rory. big meals of some monsters. beds of smelly animals. the concerns of a large animal. the

  4. English

    Can u please help me understand this poem? The Despot The garden mold was damp and chill, Winter had had his brutal will Since over all the year's content His devastating legions went. Then Spring's bright banners came there woke

  1. health

    Mark is a 30yo businessman who was diagnosed with Crohn’s dz over ten years ago; otherwise, he’s a healthy guy. He’s been free of flare-ups for the past couple of years, but a recent business trip to Thailand (stress, new

  2. English

    Identify the adverb clause and tell what it modifies. 1. Because the house had been vacant for so long, the lawn and garden were overgrown. 2. The grass in the front looked as if it hadn't been cut in months. 3. Ruth began mowing

  3. Environmental engineering

    Ottawa’s anaerobic digester produces 13 m^3/day of sludge with a suspended solids concentration of 7.8%. What volume of sludge must they dispose of each year if their sand drying beds yield a solids concentration of 35%.

  4. English: Please help

    Identify the word that best describes the underlined word which for this sentence is "the shelter" The volunteers provided the shelter with new crates, beds, and bowls for the dogs. object ****** 2.indirect object

You can view more similar questions or ask a new question.