Number of Product Options

[enduroman]

Hi I have a math question - which probably is quite basic.
I have a product that can have between 1 to 10 options. It can have the options in any combination or any number. For example it can have just the 1st option, or the 1st and 3rd or first, 2nd ,3, 4th up to 10th option. It does not matter which order the options are, for example 3,2,1 vs 1,2,3 as they are just options. For example, I have a bike that can have option1 light, option 2 water bottle holder, etc. upto any combination of the 10 options.

I am trying to work out the formula for the number of options and the best way to show them in a matrix. I have to assign each permuation a unique product number.

Thanks for help

 

[pka]

The answer has two possiblites and they only number apart.
If it is possible to have no options then the number is \(\displaystyle 2^{10}=1024\).

If there must be at least one option then \(\displaystyle 1023\).