7 stud probability question

I am trying to figure out the chances of getting a 7 card hand that is a 9 high or worse with out a straight or flush.


Can anyone help me figure this out or tell me the chances and how they got there?


thanks

stud

this is not counting an ace either so the only possible ways are

2345789 and 2346789. Any other way would result in a straight.

The only possible hands seem to be 9876432 and 9875432, or 4**7 for each. From that you subtract the number of 5-flushes, 6-flushes, and 7-flushes. For the 5-flush, there are 4 suits, 7choose5 are of that suit and the remaining 2 cards can each be of any of 3 suits; or there are 4*(7*6/2)*(2*3) 5-flushes (for non-paired hands).


Divide the above by the total number of hands which is 52choose7 or (52*51*..*46)/(7*6*..*2*1).


Good luck. What's the point?


- Louie

2 possible rank combinations, 4^7-4-4*3*7-4*3^2*comb(7,2) suit combinations out of comb(52,7) hands. Odds are 1:4303.5, p=0.0002323. About 1/4 lower than the probablility of getting a straight flush.


cu


Ignatius