In the card game bridge, each of 4 players is dealt a hand of 13 of the 52 cards. What is the probability that each player receives exactly

For the first player:

The total number of possible hands of 13 cards from a deck of 52 is ₅₂C₁₃.

The total number of possible hands for this player that contains one ace and twelve other cards:

₄C₁·₄₈C₁₂  (which is choosing 1 ace from 4 aces and 12 other cards from the 48 remaining cards)

So, the probability for the first person getting one ace is:   ( ₄C₁·₄₈C₁₂ ) / ₅₂C₁₃ 

For the second player:

Probability  =  ( ₃C₁·₃₆C₁₂ ) / ₃₉C₁₃ 

because:  there are only 3 aces left, only 36 other cards left, and only a total of 39 cards left.

For the third player:

Probability  =  ( ₂C₁·₂₄C₁₂ ) / ₂₆C₁₃ 

because:  there are only 2 aces left, only 24 other cards left, and only a total of 26 cards left.

For the fourth player:

Probability  =  ( ₁C₁·₁₂C₁₂ ) / ₁₃C₁₃ 

because:  there is only 1 ace left, only 12 other cards left, and only a total of 13 cards left.

Multiply these four probabilities together to get the total probability. ...