What is the probability of getting a flush in spades( all cards are same suit) in a poker hand of five cards?

Question

answer is 33/66640 ... but how do u get to dis answer>?

Answer 1

(13/52)(12/51)(11/50)(10/49)(9/48)
(1/4)(4/17)(11/50)(10/49)(3/16)
(1320/2665600)
(132/266560)
(66/133280)
(33/66640)

here is how they get it

13 spades out of 52, or 1 out of 4. Take 1 out and that leaves you with 12 spades out of 51, or 4 out of 17. Take 1 out and that leaves you with 11 out of 50. Take 1 out and that leaves you with 10 out of 49. Take 1 out and that leaves you with 9 out of 48, or 3 out of 16.

So this gives you
(1/4)(4/17)(11/50)(10/49)(3/16)

Multiply that all together and you get (33/66640) as your answer.

Answer 2

It's the number of hands that are all spades divided by the total number of hands.

The number of space flushs is the number of ways you select 5 spaces from the set of 13 spaces which is 13!/5!/8!

The number of total poker is the number of ways you can select 13 cards from the deck of 52 which is 52!/5!47!

So the odds are 13!/5!/8!/(52!/5!47!)

(13x12x11x10x9/5x4x3x2)/(52x51x50x49x48/ 5x4x3x2) =

(13x12x11x10x9)/(52x51x50x49x48) =
(13x12x11x10x9)/(4x13x51x5x10x4x12) =
11x3/ 4x51x5x4x4

Answer 3

13/52 * 12/51 * 11/50 * 10/49 * 9/48 = 154440 / 311875200

To reduce to lowest terms, factor out 4680: 33 / 66640

Answer 4

u have 13 cards of each suit.
prob 13 cards u r dealt with r of the same suit=(13/(13+13+13+13)) x(12/(12+13+13+13)) x(11/(11+13+13+13))x... until u get 5 cards.

I previously said 13... sorry. i didn't read the question carefully.

Answer 5

13/52*12/51*11/50*10/49*9/48=prob