When to use factorials versus simple multiplication

[sarahmoore.2009]

Can someone please help me understand why the answer to part A of this question is not 6! times 2? The answer given was 2*2*2*2*2*2=64

I think I'm having a problem, in general, of knowing how to replicate the total number of options in a given problem. I don't tend to mess up problems when it comes to differentiating between permutations and combinations, but I often make mistakes when it comes to decidingng whether to use permu/combo OR just multiply the choices/make a decision type tree. Can anyone help me out with this?

Kevin has wired 6 light bulbs to a board so that, when he presses a button, each bulb has an equal chance of lighting up or staying dark. Each of the six bulbs is independent of the other five.

(a) In how many different configurations could the bulbs on the board light up (includ- ing the configuration in which none of them light up)?

[RonPurewal]

Please don't double-post, thanks.

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