My textbook asks the question:
There are 100 distinct bikes and 4 distinct warehouses. How many ways are there to distribute the bikes into the warehouses.
What confuses me is that the order of the bikes in the different warehouses does not matter, but it matters if we put bike A in warehouse 1 or warehouse 2. So the warehouses are distinct, the number of elements per warehouse varies, and the order of elements in each warehouse doesn't matter.
Please help me figure this one out!
Actually it's simpler than you think.
For each bike you have $4$ possible destinations (each of the four distinct warehouses). So in total you have $$\underbrace{4 \times 4\times \ldots \times4}_{100 \text{ times }}=4^{100}$$ possible combinations.