I think this question involves hypergeometric distribution as number cards decease by 1 as each is dealt.
i.e. P(?AAAA) = 48/52 * 4/51 * 3/50 * 2/49 * 1/48
Maybe you could consider the cases: ?AAAA, A?AAA, AA?AA, AAA?A, AAAA? and find the probability that way.
i.e. Find the value of...