Subject: Question regarding Combinations and permutations

I am a programmer and I have a quick question. I have 5 criteria which will either be true or false. If a criterion is true it returns its ordinal representation, if false it returns 0. I then combine these results to determine where to go in my program. My question is: How can I figure out the number of combinations I will need?

In other words, if all evaluate true then my result would be 1,2,3,4,5. If all evaluate false the result would be 0,0,0,0,0. In between I need to know all possible combinations of ordinal number and zero there can be (1,2,3,4,0; 1,0,3,4,0; etc)

Thank-you
Paul Stoner

Hi Paul,

Each of your criteria evaluate either true or false, that is they each have two possible options (I'm assuming here that one criterion cannot return the ordinal representation of another criterion). Since you have two choices for the first criterion, then two choices for the second, .... and finally two choices for the 5th criterion, your total number of possible outcomes will be 2*2*2*2*2 = 2⁵ = 32.

Cheers, Patrick