Three players are each dealt, in a random manner, five cards from a deck containing 52 cards. Four of the 52 cards are aces. What is the probability that at least one person receives exactly two aces in their five cards?
Let $A_i$ represent the player $i$ with two aces where $i = 1,2,3$. The probability a player receives two aces is the following. $P(A_i) = \frac{{4 \choose 2}{48 \choose 3}}{{52 \choose 5}} \approx .0399$
Then the probability at least one person receives exactly two aces is the following. $3 \cdot .0399 - 3 \cdot .0399^2 \approx .1149$
Is this correct?