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# help

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Matt's four cousins are coming to visit. There are four identical rooms that they can stay in. If any number of the cousins can stay in one room, how many different ways are there to put the cousins in the rooms?

May 31, 2019

#1
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You can solve this using sticks and stones strategy.

However I am going to do case work because its simpler

Case 1: There is maximum 1 person in each room

Obviously 4! so 24 for case 1

Case 2: There are maximum 2 people in each rooms

So we can list possiblities

If ONLY 2 or 0 people can be in a room, then it is 2! => 4

If 2, 1, and 0 people can be in a room, then it is 3! => 6

So 10 cases for case 2

Case 3: There are Maximum 3 people in each room

Just like case 2 we can list possibilities

If ONLY 3, 1, and 0 people can be a room then it is 3! => 6

Thats all for case 3 so we have 6 because some of our possibilities were already done for case 2

Case 4: There are 4 people in one room with three other empty rooms

Obviously 4.

To find the answer we won't multiply the cases we will add them.

4+6+10+24 = 44 ways we can put 4 people in 4 bedrooms.

May 31, 2019
#2
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Someone check this

CalculatorUser  May 31, 2019