15 cards can be arranged in 307,674,368,000 ways (factorial 15, 15 X 14 X 13, etc.).
What is the probability that if 15 cards consisting of a royal flush in spades, a royal flush in diamonds and the 5, 6, 7, 8, 9 in hearts will, after a random shuffle, end up in this order from top to bottom as the cards are held face down:
5, 6, 7, 8, 9 of hearts, 10, J, Q, K, A of spades, 10, J, Q, K, A of diamonds.
Probability Question

 Posts: 2096
 Joined: January 17th, 2008, 12:00 pm
 Location: Short card above selection.
Re: Probability Question
Is this that old "reverse polynomial factored Fibonacci integer" joke?

 Posts: 427
 Joined: February 7th, 2008, 12:00 pm
 Location: Brooklyn NY
Re: Probability Question
If you want that exact order then of course 1 out of 15 factorial.
But if you don't care about the order within the suits, but do care about all the cards of one suit being together and in that particular suit order, then your probability increases to 120x 120x 120 out of 15 factorial.
But if you don't care about the order within the suits, but do care about all the cards of one suit being together and in that particular suit order, then your probability increases to 120x 120x 120 out of 15 factorial.

 Posts: 2096
 Joined: January 17th, 2008, 12:00 pm
 Location: Short card above selection.

 Posts: 41
 Joined: December 24th, 2015, 10:29 am
 Favorite Magician: Paul Megram
Re: Probability Question
What Jack said. 1 in 15! , or 5! cubed in 15!, depending on your criteria.
Dave
Dave

 Posts: 36
 Joined: July 26th, 2008, 10:07 pm
Re: Probability Question
Point of order: It may have been a typo in the original post but for the sake of accuracy in calculations with respect to this probability question, 15! actually works out to equal 1,307,674,368,000.
 Matthew Field
 Posts: 2732
 Joined: January 18th, 2008, 12:00 pm
 Favorite Magician: Slydini
 Location: Hastings, England, UK
Re: Probability Question
When I do that 15! bit I always use the out "Off by 1."
Matt Field
Matt Field

 Posts: 2096
 Joined: January 17th, 2008, 12:00 pm
 Location: Short card above selection.
Re: Probability Question
Would that be 1,307,674,368,000 in the trillions? My math abilities are sadly deficient.
Is there an online calculator for factorials?
Is there an online calculator for factorials?
 Brian Douglas
 Posts: 41
 Joined: November 19th, 2016, 10:34 am
 Favorite Magician: Salguod Nairb
 Location: Middle East
 Contact:
Re: Probability Question
The probability will be 50  50. Either it will happen or it won't.
Everything else is horseshoes and hand grenades.
Everything else is horseshoes and hand grenades.
 Steve Bryant
 Posts: 1821
 Joined: January 17th, 2008, 12:00 pm
 Favorite Magician: Ballantine
 Location: Bloomington IN
 Contact:
Re: Probability Question
Re "Is there an online calculator for factorials?"
go to google and type What is 15!
The answer pops up in an online calculator. This is neat!
go to google and type What is 15!
The answer pops up in an online calculator. This is neat!

 Posts: 627
 Joined: June 7th, 2015, 12:48 pm
 Favorite Magician: Bill Malone
 Location: Santa Rosa, California
Re: Probability Question
Bob wrote:"1,307,674,368,000 in the trillions?"
Yes, one trillion, 307 billion, 674 million, 368 thousand
Easy way to figure is to first segregate the number on the right that is in the hundreds of thousands (in this case 368,000). Then working your way LEFT, the next threedigit number is in the millions (here 674 million) then the next threedigit number is in the billions (here 307 billion) then finally the next number to the left (irrespective of the number of digits) is in the trillions (here one trillion)
Yes, one trillion, 307 billion, 674 million, 368 thousand
Easy way to figure is to first segregate the number on the right that is in the hundreds of thousands (in this case 368,000). Then working your way LEFT, the next threedigit number is in the millions (here 674 million) then the next threedigit number is in the billions (here 307 billion) then finally the next number to the left (irrespective of the number of digits) is in the trillions (here one trillion)

 Posts: 2096
 Joined: January 17th, 2008, 12:00 pm
 Location: Short card above selection.
Re: Probability Question
Wow. That's great. I have a card trick that has once chance in one trillion, 307 billion, 674 million, 368 thousand of being successfulhowever, the magician triumphs and is successful. It will be in a manuscript I'm working on entitled, "Tarodiction." This will include an extensive development of what, up to now, has been a principle that has seen very little, if any use, for magic. Will advise when available. If you are interested in cards, the manuscript will be invaluable.