Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a 4, the second card is a $\clubsuit$, and the third card is a 2?
Is there an efficient way to do this with cases? If so, how? Is there any other way to do this problem without cases?
So for the 4 is club and 2 is club case I have 1/52 * 11/51*1/50.
For the 4 is club and 2 is not club case I have 1/52*12/51* 3/50.
For the 4 is not club and 2 is club case I have 3/52 * 12/51 * 1/50.
For the 4 is not club and 2 is not club case I have 3/52 * 13/51*1/50.
My final answer is 122/132600 = 61/66300. Why am I wrong?