SOLUTION: The question is: A poker deck consisting of 52 cards, representing 13 denomination and 4 suits. A 5 card hand is called a flush if all cards are the same suit but not all 5 denomi

Question 469239: The question is: A poker deck consisting of 52 cards, representing 13 denomination and 4 suits. A 5 card hand is called a flush if all cards are the same suit but not all 5 denominations are consecutive. You have drawn a 2 of hearts,3 of hearts, 7 of hearts, jack of hearts and a queen of hearts. Let N be the set of 5 cards in hearts that are not flushes. How many outcomes are in N?
I am assuming we need to find the probability of having a flush in hearts.
Card 1: .25, card 2:.24, card 3: .22, card 4: .20 and card 5: .19.
.25*.24*.22*.20*.19=.0005016
I don't know my next steps.
Found 2 solutions by edjones, ccs2011:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let N be the set of 5 cards in hearts that are not flushes.
The set N is called a straight flush. They beat any other poker hand including a flush.
There are 10 possible straight flushes in a suit A2345 to TJQKA.
There are 4 different suits.
10C1 * 4C1 = 40 possible straight flushes.
.
Ed
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
N is the set of possible straight-flushes in hearts.
We are assuming all cards are hearts.
For the hand to be a straight all cards must be in consecutive order.
A-2-3-4-5
This is the lowest possible straight, the highest possible straight would yield a royal flush
10-J-Q-K-A
The number of cards from A to 10 is 10 cards
Therefore there are only 10 possible straights with 5 hearts.
10 outcomes in N

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