five windows

some open, some closed
how many different arrangements can there be

To determine the number of different arrangements of the five windows, given that some are open and some are closed, we can use combinatorics.

First, let's define a few terms:
- "Arrangement" means the order in which the windows are arranged.
- "Open" means the window is opened.
- "Closed" means the window is closed.

In this case, there are two options for each window: it can either be open or closed. Since we have five windows, and two options for each window, we can calculate the total number of arrangements by raising 2 to the power of 5 (since 2 options for each of the 5 windows).

Hence, the number of different arrangements can be calculated as:
2^5 = 32

So, there can be 32 different arrangements of the five windows, with some windows open and some closed.