In a deck of 52 playing cards, what is the probability of drawing four cards of the same rank?
To solve this problem, we need to use the concept of combinations. First, let's determine the total number of ways to draw four cards from a deck of 52 cards without any restrictions:

Total combinations = C(52, 4) = 52! / (4!(52-4)!) = 270,725

Now, let's find the number of ways to draw four cards of the same rank. There are 13 ranks in a deck (Aces, Twos, ..., Kings), and for each rank, there are 4 cards (one from each suit). So, we need to choose one rank out of 13 and then select all 4 cards of that rank:

Combinations of four cards with the same rank = C(13, 1) * C(4, 4)
                                                             = 13! / (1!(13-1)!) * 4! / (4!(4-4)!)
                                                             = 13

Finally, we can calculate the probability of drawing four cards of the same rank by dividing the number of combinations with the same rank by the total number of combinations:

Probability = Combinations of four cards with the same rank / Total combinations
                   = 13 / 270,725
                   ≈ 0.000048

So, the probability of drawing four cards of the same rank is approximately 0.0048% or 1 in 20,817.