Using random binary #s to select random item from odd-numbered list

I'm fairly new to programming and have a general computer programming logic that's been bugging me. This is just a logic problem that I've been trying to figure out as an exercise; not really a practical problem.

I have a stream of random binary numbers. I want to come up with an efficient code (I know there are many inefficient ways to do this) to use the random binary numbers to select a random item from a list of any length. Doing this with an even-numbered set is easy; you just use the 0 or 1 to keep splitting the list until you get a random number.

But doing this with an odd-numbered list has been surprisingly difficult. Maybe this is an actual difficult thing to do or maybe I'm just missing some logical step that's very obvious to experienced programmers.

Thanks to anyone who can help!

Zach
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