probability of a flush?

#1
hey guys, so I worked out this problem but i'm just wondering if I am right and maybe how much further in depth I may need to go

Question: suppose your first thee cards are all diamonds. (you are playing 7 crad stud) What is the probability of getting a flush? (hint: you will have a flush if you finish with five, six or seven diamonds. you won't be able to get a flush in any other suit)

I worked out that the probability of getting 5 diamonds was 1287/2598960 which is 0.000495 but I was wondering if that's right how much farther I have to go to complete the question and how I would go about doing that? thanks
 

JohnM

TS Contributor
#2
Use the same tree-diagram process that I described previously in your higi-low stud problem:

Start with a hand of three diamonds. There are 49 cards left. How many more diamonds are left? How many more "non-diamonds?" Draw the branches and determine the probabilities.

Then do the next card, branching again from the original two branches. There will be 48 cards left - based on the first set of branches, how many diamonds would be left and how many "non-diamonds?" - use this info to determine the conditional probabilities.

...and so on and so on until you get branches with at least 2 more diamonds - terminate these branches. Also terminate branches where you get enough "non-diamonds" to make a flush impossible.