probability of a run in pinochle

[rjay]

i'd like to know the probability of attaining a run, i.e., an Ace, Ten, King, Queen, & Jack in the same suit from a deck of 48 cards in a single pinochle deck which consists of eight each of aces, tens, kings, queens, jacks and nines.
i thought the factors might be as follows:

40/48 -> any card but a nine
8/47 -> if 1st card is 10 of clubs, there are eight desirable clubs left, i.e., AC,KC,QC,JC (2 of each)
6/46 -> 6 desirable clubs left
4/45 -> 4 desirable clubs left
2/44 -> 2 clubs left
but i don't care what order the cards are received in, so i believe there would be 5! ways of arranging the five cards...which led me to think of the following probability:

40/48*8/47*6/46*4/45*2/44*5! ~= .00897

but i'm not confident with that result and think it should be better than that, maybe about 2 or 3 % instead of less than 1%.

btw, i don't care what the other cards are and there are 11 cards dealt to each player (4 players) and four cards in the "kitty"

any help would be greatly appreciated

robert