Jack, Queen, King and Ace are the top cards.
What is the probability of getting three top cards in the same suit and two cards in another suit (but both in the same suit)?
This has stumped me for ages, I can get the answer if there is no "top cards" bit with them I am getting ridiculously small numbers. Any help?
Assuming you are drawing a $5$ card hand from a standard deck of $52$, there are $4$ ways to choose the suit of the top cards, $4 \choose 3$ ways to choose which three, $3$ ways to choose the other suit, and ${13 \choose 2}$ ways to choose the other two cards. The total probability is then $$\frac {4 {4 \choose 3} 3 {13 \choose 2}}{52 \choose 5}=\frac 6{4165}$$