1. A dental floss device and applicator assembly comprising: (a) a pair of separate, substantially elongate members, each of said members having spaced apart top and bottom end portions with a gripping section located between said top and bottom end portions; (b) a plurality of dental floss segments; (c) attachment means on each of said top end portion for releasably holding one of said dental floss segments (STRAND) without requiring a user to manipulate with said user's fingers said STRAND to attach said STRAND to said attachment means, said attachment means comprising a slot formed in said top end portion and a groove formed in said top end portion and located adjacent to said slot, said groove having means for releasably holding said STRAND within said groove and guiding said STRAND to said slot, said slot having a first prong protruding from said slot for releasably holding said STRAND within said slot; (d) a container for storing said dental floss segments and comprising spaced apart opposite sides having a plurality of spaced apart support means attached to said spaced apart opposite sides for releasably holding said dental floss segments, said support means releasing said STRAND from said container when said user presses said top end portion of said members against said STRAND whereby said attachment means releasably holds said STRAND; and (e) said members being of sufficient length to allow said user to insert said members into a person's mouth with said STRAND attached to said top end portion of said members to clean all surfaces of said person's teeth without requiring said user to insert said user's fingers into said person's mouth, said user not having to manipulate said STRAND with said user's fingers when cleaning said person's teeth.