Question

Please can You help!
A poker hand (Five cards) are dealt. i-) Find the chance that the cards are all of the same suit. This is sometimes called a flush.
My Solution approach had been:
There are 4 ways of picking a suit from the four (4C1 = 4), so there are 4 ways of getting a royal flush. Again, assuming the deck is well-shuffled, the chance of a royal flush is 4/(52C5)= 4/2598960=??? is this ok???

Answer 1

the question is asking about a flush [not necessarily a royal one],

Answer 2

what is difference can you explain!

Answer 3

well \[\{\spadesuit 2,\spadesuit 4,\spadesuit 8,\spadesuit 10,\spadesuit 2K\}\] is a Flush because the five cards are all of the same suit,


\[\{\clubsuit 2,\clubsuit 3,\clubsuit 4,\clubsuit 5,\clubsuit 6\}\]is also a flush,
but all the cards are consecutive; so it is a Straigtht flush

\[\{\color{red}{\heartsuit10},\color{red}{\heartsuit J},\color{red}{\heartsuit Q},\color{red}{\heartsuit K},\color{red}{\heartsuit A}\}\]is also a Straigtht flush,
but because it is the highest possible straight flush it is a Royal Flush

Answer 4

your right that there are only four ways to get a straight flush, but there are many more was to simply get a Flush

Answer 5

to get a flush , the first card can be any card of any suit, the next four card must be of this same suit.

Answer 6

then
( 13C1 * 12C1 * 4C1 )/ (52C5)= 13×4×12 = 624/2598960=???OK

Answer 7

To get a flush, you need to get 5 diamonds/spades/clubs/hearts from 13.

So from 13 cards of one suit, choose 5. There's four different suits, so you can multiply that by 4 (4C1). Then divide by the total number of possible 5 card hands.

\[\large \frac{ 4C1 \times 13 C 5 }{ 52 C 5 }\]

Answer 8

Please can you quantify 13C5=

Answer 9

Aren't you able to work it out? You worked out 52C5 in your original question...
http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html

Answer 10

13C5=1287 Thanks