[jay_shark]

One approach is to use the inclusion/exclusion .

P(AuBuC) = P(A) + P(B) +P(C) - P(AB) - P(AC) - P(BC) + P(ABC).

Where P(AuBuC) = the probability of event A or event B or event C happening .

P(AB)= the probability of event A and event B happening together .

So Let us define what these letters mean in this context .

Let A denote the event that the first card is an ace or a king .
B is the event that the second card is an ace or a king .
C is defined similarly .

P(AuBuC) = 6/48+ 6/48 + 6/48 - 3*[2*3/48*3/47 + 2*3/48*2/47]
+ [3/48*2/47*3/46*3*2 + 3/48*2/47*1/46*2]

= 0.336262719

The tricky part is to figure out the probabilities of the joint events happening .

i.e, P(AB) = the probability the first card is an ace (3/48) , times the probability the second card is a K ( 3/47) . However the reverse may be true as well and we multiply by 2 . Moreover , the probability the first card is an ace followed by a second ace is 3/48*2/47 . The same is true for kings and so we multiply that by 2 .

Solution 2: This is the easiest approach .

The probability the flop does not contain an A or a K is (48-6)C3/48c3 . Therefore the probability the flop contains an A or a K is the complement of that or 1 - 42c3/48c3 = 0.336262719 .