The Collaborative International Dictionary of English v.0.48:

Promiscuousness \Pro*mis"cu*ous*ness\, n.
   The quality or state of being promiscuous.
   [1913 Webster]

WordNet (r) 3.0 (2006):

promiscuousness
    n 1: indulging in promiscuous (casual and indiscriminate) sexual
         relations [syn: promiscuity, promiscuousness, sleeping
         around]