Mcharles

[Guest]

Hello. I'm looking to confirm an answer I came up with. I'm pretty sure this is going to seem really silly to many of you because it's probably very easy for you to understand, but I can't wrap my head around it.

Here is the scenario.

You have 23 lights, each with its own switch.
Each switch functions like almost all light switches, each switch is either, "ON" or "OFF."
How many unique combinations of the lights being "ON" or "OFF" are possible?

So I'm thinking since each switch has only 2 settings, the way to come up with the total possible combos is 2^23 (2 to the 23rd power).

So this comes out to 8,388,608 total.

This number seems incredibly high to me. Looking at these 23 switches in front of me (for my kid's school project) I just can't believe there are nearly 8.4 million combos possible. I.must be doing something wrong???

Any help or confirmatiin is greatly appreciated.
Thx in advance.
Charles

[HallsofIvy]

Yes, with 23 switches, each of which can be "on" or "off", independent of what the other switches are, there are [tex]2^{23}[/tex] possible positions. Yes, that is 8,388,608. I just don't understand why you are surprised at that.