Math

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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.

  • Math -

    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.

    9!/(4!3!2!)=1260

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