Respuesta :
The total number of different ways there are to put the cousins in the rooms is; 15
How to use probability combinations?
When we count the number of cousins staying in each room, it means that the possibilities are as follows; (4,0,0,0), (3,1,0,0), (2,2,0,0), (2,1,1,0), (1,1,1,1).
1) (4,0,0,0): This means that there is only 1 way to put all the cousins in the same room due to the fact that the rooms are identical.
2) (3,1,0,0): This means that there are 4 ways to choose which cousin will be in a different room than the others.
3) (2,2,0,0): This means that there are 3 ways to choose which of the other cousins will also stay in that room, and then the other two are automatically in the other room.
4) (2,1,1,0): This means that the number of ways to choose which cousins stay in the same room is; 4C2 = 6
5) (1,1,1,1): This means that there is only one way for all the cousins to the total number of possible arrangements is;
1 + 4 + 3 + 6 + 1 = 15each stay in a different room.
Therefore, the total number of possible arrangements is;
1 + 4 + 3 + 6 + 1 = 15
Read more about Probability Combinations at; https://brainly.com/question/3901018
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