How many distinct binary bit strings of length fifteen are there? I know this is a simple question but i'm not sure of which combinatorial selection equation to use.
How many distinct binary bit strings of length fifteen are there?
Using a simple example, would someone be able to explain the difference between


*

*orded with repetition

*orded without repetition

*unorded with repetition

*unorderd without repetition


I have had a look around but none of the examples are making much sense.

With  binary strings of length $15$ you can't have without repetition.  There are only two characters, so by the third character you will have repetition.  If the string is not ordered you only care how many $0$s and $1$s there are.  The number of $0$s can range from $0$ to $15$-how many is that?  Then the number of $1$s is determined.  For ordered strings, each bit has two choices, so there are $2^{15}$
