I would like to find all the expressions that can be created using nothing but arithmetic operators, exactly eight $8$'s, and parentheses. Here are the seven solutions i've found (on the internet) The way you're getting your bounds isn't a useful way to do things. You've picked the two very smallest terms of the expression to add together; On the other end of the binomial expansion, you have terms … A hypothetical example: You have a 1/1000 chance of being hit by a bus when crossing the street.

Understanding the Context

However, if you perform the action of crossing the street 1000 times, then your chance of being