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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

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

Someone check this

CalculatorUser  May 31, 2019

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