Puzzle #162: Swimsuit Issue

If Sports Illustrated can do it, so can I.

You have eight bikinis, each of a different colour. Four are string bikinis and four are not. Of course, you can mix and match. Here are the rules. The top’s colour must be the same as the bottom’s or precede the bottom’s colour in alphabetical order. A string bottom can be paired with a non-string top, but a non-string bottom can not be paired with a string top.

How many possible bikini top and bottom pairs are there? (Actually, this is indeterminate and depends on which colours in the colour order are string and non-string.)

The real question: What are the minimum and maximum numbers of possible bikini top and bottom pairs allowed? For both numbers, what is the arrangement of string and non-string in the colour order?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, July 13, 2016 at noon Pacific Time. I will post the answer shortly after.