To rank 11 persons subjectively by comparing each person with every other person, we need to determine the number of unique pairs that can be formed from a group of 11. This is a combination problem, specifically "11 choose 2", as the order of comparison does not matter (comparing A with B is the same as comparing B with A). The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items, and r is the number of items to choose. In this case, it's 11C2 = 11! / (2! * 9!) = (11 * 10) / (2 * 1) = 110 / 2 = 55.