are you looking for JUST one diamond or AT LEAST one diamond? it's a big difference

 

sorry i didn't clarify... at least 1 diamond... there can be 1 diamond or they can all be diamonds.

 

i say the answer is 82251/270725

 

oops that's the possibility of have 0 diamonds. so it's 1 - 82251/270725

 

wait, but where does that come from ?

 

have you learned combinations? C(39,4) = 39!/35!/4! = 82251

39 stands for total number of non-diamonds. 4 stands for cards you're choosing.

and C(52,4) = 52!/48!/4! = 270725 is the total number of 4 hand possibilities.

 

let me also just give some background to what this is all about... my friend and i were just playing heads up poker, and there were 4 diamonds on the board, and neither of us had a diamond, and he said "what are the odds that neither of us (we each had 2 hole cards) didn't have a diamond" ... so he said that it should be a 100% chance that one of the 4 cards (we realized that it made a difference that there were 4 already on the board, so we were speaking specifically just 4 random cards from a new deck). anyway that just didn't make sense, so that's why i'm turning to you guys

 

interesting story.. i wonder sometimes myself but too lazy to actually calculate anything.. i thought this was for homework or something =P

 

im pretty sure you learn this in statistics, thrs a certain equation i believe.

 

i declare myself the winner


since i did it first, my answer is right