  We present an alternative proof to the Touchard-Kaplansky formula for the
probl\`eme des m\'enages, which, we believe, is simpler than the extant ones
and is in the spirit of the elegant original proof by Kaplansky (1943). About
the latter proof, Bogart and Doyle (1986) argued that despite its cleverness,
suffered from opting to give precedence to one of the genders for the couples
involved (Bogart and Doyle supplied an elegant proof that avoided such
gender-dependent bias).
