Total number of ways to distribute Aces is: $\displaystyle {7 \choose 4}=35$

4 aces in one player's hands:

(4,0,0,0) = 4 ways

3 aces in 1 player's hands:

(3,1,0,0) = 12 ways

2 aces in 1 player's hands:

(2,2,0,0) = 6 ways

or

(2,1,1,0) = 12 ways

1 aces in each player's hand:

(1,1,1,1) = 1 way

Total is 35 ways.

But can anybody tell me how to calculate the probability of each scenario happening? Say, (2,1,1,0).

Thanks