OK, so I am having a little problem with a question about probability, an area I am not good at. The problem goes like this:
You draw 5 cards separately without replacement from a standard deck of 52 cards. What is the probability that the colors alternate after each card? Ex. Black, Red, Black, Red, Black. I tried two methods, but they both give me different answers.
Method 1 (Multiplication):
$P=1\times \frac{26}{51}\times\frac{25}{50}\times\frac{25}{49}\times\frac{24}{48}=\frac{325}{4998}$
Method 2 (Combinations):
$\frac{{26\choose3} {26\choose2}}{{52}\choose{5}}=\frac{1625}{4998}$
I don't know which one is right, but I can guess it is the first one. Can you help me and tell me how I went wrong with either one of them, or both?