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Question : five backpackers arrive in a city where there are 5 youth hostels

How many different accomodation arrangements are there if there are no restrictions on where a backpacker stays ?

I tried this but I can't seem to get your answer in the textbook which is 5^5

user122343
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  • Maybe this will help... let's say there are 5 backpackers but only one 1 youth hostel. So everyone has to sleep there. Then the first guy has only 1 choice, the second guy has 1 choice, etc. So there's $11111$ different accommodations. Or let's say there's only 1 backpacker and 5 different youth hostels. Then there are 5 different arrangements. I dunno I hope that helped! =) – HJ_beginner Aug 26 '18 at 06:21

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The first backpacker has five youth hostels to choose from. So does the second, third, fourth, and fifth since there aren't any restrictions on where they stay. So there are $5\times 5\times 5\times 5\times 5=5^5$ possible arrangements.