I encountered these two problems and am wondering why we cannot use the same strategy to solve both.
The first one is
You are dealt a hand of four cards from a well-shuffled deck of 52 cards. Specify an appropriate sample space and determine the probability that you receive the four cards J, Q, K, A in any order, with suit irrelevant.
and the textbook solution for this is $\frac{\binom{4}{1}\binom{4}{1}\binom{4}{1}\binom{4}{1}}{\binom{52}{5}}$.
The second problem is
You draw at random five cards from a standard deck of 52 cards. What is the probability that there is an ace among the five cards and a king or queen?
But here, using the same kind of formula to get one ace out of four possible, and one queen or king out of 8 possible, so $\frac{\binom{4}{1}\binom{8}{1}\binom{39}{3}}{\binom{52}{5}}$, leads to the wrong answer than the one in the textbook.
What is the difference between these two problems and why is the intuition for the second one wrong? Thanks!