Dear Esteemed Forumers. I couldn’t quite understand why we multiplied by 2^6. I thought it will be 10 x 2 x 2 x 2 x 2 x 2 x 1 because one of the 6 optional toppings, we only have one option, hence 1. Instead, the solution proposes that we multiplies like usual and only minus 1 from the final answer.

I don’t get what you mean by that. For each topping, you have two options - yes or no.

Thanks for the reply =) I make it multiplied by 1 because I assume that at least one toppings has to be a no or at least 1 of the option for toppings is restricted to 1, hence 10 x 2^5 x 1.

Not true, and even if that was the case, you would consider that case individually and substract from all cases.

Put it this way: if it was “at least zero toppings has to be a no”, would the number of ways be 0?