1. 
[syn: randomly, indiscriminately, haphazardly, willy-nilly, arbitrarily, at random, every which way]
The Collaborative International Dictionary of English v.0.48:
Arbitrarily \Ar"bi*tra*ri*ly\, adv.
   In an arbitrary manner; by will only; despotically;
   absolutely.
   [1913 Webster]
WordNet (r) 3.0 (2006):
arbitrarily
    adv 1: in a random manner; "the houses were randomly scattered";
           "bullets were fired into the crowd at random" [syn:
           randomly, indiscriminately, haphazardly, willy-
           nilly, arbitrarily, at random, every which way]