Question

the number of functions defined 10 points are possible if its functional value is either 0 or 1​

Answer 1

Answer:

This is from the text A First Course on Probability by Sheldon Ross.

The solution he provides is:

Let the points be 1,2,...,n. Since f(i) must be either 0 or 1 for each i=1,2,...n, it follows that there are 2n possible functions.

I don't understand where he gets 2n from...can you elaborate more on this? Is there a different way to solve this problem, a longer, more detailed, and clearer way?