There are 52 cards in bridge and 13 cards of each suit. The formula for numerator is: $${13\choose a}{39 \choose 13-a}{13-a\choose b}{26+a\choose 13-b}{13-a-b\choose c}{13+a+b\choose 13-c}$$
But i don't understand why must we add back a and a+b for the rest cards(i mean $${26+a\choose 13-b}$$ and $${13+a+b\choose 13-c}$$
I thought that we have dealt this spades for other players. Explaint me please this formula Thank you