While Simon Cowell is frolicking on the beaches of Barbados with his former fiancée, Mezhgan Hussainy, his new flame, Carmen Electra, is spending New Year’s in Las Vegas. She’ll appear at Simon Hammerstein’s theater show, The Act, at The Shoppes at the Palazzo tomorrow and on Fox’s “New Year’s Eve Live” special. Last week, the unchivalrous Cowell told Ryan Seacrest’s radio show that he and Electra aren’t exclusive. “She’s not my girlfriend,” “The X Factor” creator stated. “We’re people who date.”