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 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?

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: $$ 1 - \mathbb P(A) = \frac{3072401}{11881376}\approx 0.2585897. $$