A 5-card poker hand is dealt from a well shuffled regular 52-card playing card deck. Find the probability that the hand is a Flush (5 nonconsecutive cards each of the same suit).

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A 5-card poker hand is dealt from a well shuffled regular 52-card playing card deck. Find the probability that the hand is a Flush (5 nonconsecutive cards each of the same suit).

Mathematics
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|dw:1442546703792:dw|
you are very artistic my friend
chance of 5 cards being all diamond + 5 cards being all heart, all clubs , all spades

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Other answers:

|dw:1442546916458:dw|
|dw:1442546963874:dw|
4 ways to choose a suit * 13 * 12 * 11 * 10 * 9 then divide by 5! because order does not count
|dw:1442547007019:dw|
( 4 * 13 * 12 * 11 * 10* 9 / 5! ) / (52 choose 5 )
the same probability with the other suits so 4*(13*12*11*10*9/(52*51*50*49*48))
so would it be 4(99/199920)
( 4 choose 1 * 13 choose 5 ) /( 52 choose 5 ) =
.00198
i need a fraction
5148/2598960
= 33/ 16660 , oh cool 666
it says that 5148/2598960 is wrong
you must also subtract the case where the cards are consecutive from this as that would be a straight flush or a royal flush
so how is this done?
combinatorics is just logic really
you have to be able to reason through this stuff
lets take one consecutive flush, like A,2,3,4,5 what is the chance this is drawn
33/16660 is wrong?
need to subtract the consecutuve 5 card case from it jay
okay so this is how i think you should build up the consecutive case there are 13 pairs of 5 consecutive cards for example A,2,3,4,5 2,3,4,5,6 3,4,5,6,7 . . . Q,K,A,2,3 K,A,2,3,4 what is the chance of each of these cases
non straight flushes
( (4 choose 1)*(13 choose 5)-4*10 ) / ( 52 choose 5 )
close
there are 10 straights A,2,3,4,5 2,3,4,5,6 3,4,5,6,7 4,5,6,7,8 5,6,7,8,9 6,7,8,9,10 7,8,9,10, J 8,9,10, J, Q 9,10, J, Q, K 10, J, Q, K, A
well im not sure they consider KA234 consecutive too actually
1277/649740
KA234 is a wheel, thats not allowed in texas hold em poker, and most poker variants
if I was you id try these 3 solutions for your answer ( (4 choose 1)*(13 choose 5)-4*9 ) / ( 52 choose 5 ) ( (4 choose 1)*(13 choose 5)-4*10 ) / ( 52 choose 5 ) ( (4 choose 1)*(13 choose 5)-4*13 ) / ( 52 choose 5 )
well I have three attempts remaining
lol
dont make any calculation mistake xD one of those is definately right haha
is the 4*10, mean multiply or 4^10?
40
okay thank you
I think you should understand the solution before just answering
I do now
would the first one's calculation come out to be 5112/2598960
you can use wolfram as a calculator http://www.wolframalpha.com/input/?i=%28+%284+choose+1%29*%2813+choose+5%29-4*10+%29+%2F+%28+52+choose+5+%29

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