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
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.