A binomial pair is an expression containing two words which are joined by a conjunction (usually ‘and’ or ‘or’). E.g. up and down, in and out, true or false, more or less. Important: The word order of a binomial pair is usually fixed. E.g.
We drove up and down the same street ten six times or more looking for her house. [correct]
We drove down and up the same street ten six times or more looking for her house. [incorrect]