How many variations can a 10 hole punch card have?

There are 2 states for each hole (unpunched or punched).

With 10 holes, the total ways to punch the card (including leaving all holes unpunched) is:

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2¹⁰

= 1024 ways

This is also known as the "subset formula".

With a set of n items, the total number of subsets of those items is 2ⁿ. Again, you basically think that each item can be included in the set or excluded. There are 2 states for each of 10 items → 2¹⁰ = 1024 subsets.

The number to the power the number   Two lights have 4 combination, and three lights will have nine.

Peace.

If you can punch a hole or not independently of the other holes then that is 2^10, and if you google "how many combinations" you get a lot of things about combinatorics so I guess combinatorics?