A single card is drawn at random from each of six well-shuffled decks of playing cards. Let
$A$ be the event that all six cards drawn are different.(a) Find $P(A)$.
(b) Find the probability that at least two of the drawn cards match.
For (a), since each card is different, the probability is
$$\frac {\text{number of favorable cards}} {\text{total number of outcomes}}=\frac{52*51*50*49*48*47}{52^{6}}.$$
For (b), what's the logical thinking process to solve this?
Best Answer
For $(a)$, we have $$\mathbb P(A) = \frac{\frac{52!}{(52-6)!}}{52^6} = \frac{8808975}{11881376} \approx 0.74141.$$
For $(b)$, this is simply the complementary probability: $$ 1 - \mathbb P(A) = \frac{3072401}{11881376}\approx 0.2585897. $$