Relative order in a row

A fixed position names a particular place; relative order only says which named object occurs first. Other objects may lie between them. Pair each arrangement with the one obtained by swapping two named distinct objects. Exactly one arrangement in each pair has the first named object before the second, so half of all rows have the required relative order. For restrictions, fill fixed places first. Next apply any before/after test to the remaining freely interchangeable named objects. Multiply only counts for choices that can all occur. Among five distinct people including Ana and Ben, there are 5!=120 rows and 120/2=60 with Ana before Ben. They need not be adjacent. Check: “Ana before Ben” does not mean “Ana immediately before Ben”. If a fixed-place condition destroys the swap pairing, count the cases directly.