Stats and prob on cards

Question

The entire deck is equally distributed amongst 4 players. Find the probability that each player gets an ace and a king

Answer 1

There are 4! possible arrangements of each of the aces and kings, and 44!/(11!)^4 arrangements of the other cards.

We divide this by 52!/(13!)^4

This equals 24^2*44!/(11!)^4/(52!/(13!)^4) =

24^2 * (13*12)^4/P(52,8) =

2^14*3^6*13^4/(2^8*3^4*5^3*7^2*13*17*23*47) =

2^6*3^2*13^3/(5^3*7^2*17*23*47) =

1265472/112559125 =

0.0112