how does 5c1 work?

[howzit]

like if something is 5c1 or whatever it is, how does it work mathmatically.

[arras]

Boy i've been wanting to ask this for a long time. Thanks.

[Loonbat]

nCr = n! / [r!(n-r)!]

5c2 = 5!/(2!3!) = 10

10c8 = 10!/(8!2!) = 45

Get it?

[Skribbles]

Alright.... what the hell does the ! mean?

[arras]

Alright.... what the hell does the ! mean?

I think 5! means 5 x 4 x 3 x 2 x 1 ? correct?

[Loonbat]

yup yup ...

5c2 would compute as

5!/(2!3!) = (5x4x3x2x1)/[(2x1)(3x2x1)] = 120/[(2)(6)] = 10

[Skribbles]

Alright. And how do you use that in regards to Poker?

[Loonbat]

One example:

52c5 will give you the number of unique 5-card hands that there are.

[ShoelessJoe]

I know that n stands for 'number of units'

but what do c/C and r stand for?

[Prodigy]

Alright.... what the hell does the ! mean?

I think 5! means 5 x 4 x 3 x 2 x 1 ? correct?

..yea ! is..if i remember correctly is "factorial" and its multiplied by every number up to that starting with 1

e.g. 3! = 3 x 2 x 1
6! = 6 x 5 x 4 x 3 x 2 x 1

[suitedaces84]

I know that n stands for 'number of units'

but what do c/C and r stand for?

c/C stands for choose. This is the name of the funtion, it's the equivalant of +, -, * or /. n and r are like X and Y. When using the choose funtion they must be positive integers because it's impossible to have a fraction of a card or a negative card. The greater number always goes first. Let's say there are 52 cards in my deck (although I've often been accused of not playing with full deck, whatever that means ). If I pick out 5 cards at random there are 52c5 combinations of cards I could pick out (order unimportant). If there were X number cards in my deck and I ramdomly selected Y number of cards (note: Y obviously cannot be greater than X) there would be XcY different combinations.

I think he used C one time and c another time to avoid having it look funny.

[Loonbat]

"C" stands for "combination" (versus "P" for permutation).

A combination doesn't allow a repeat ... it assumes that As Ks Qs Js and Ts is the same hand as Ks As Ts Js and Qs (which of course, it is). Mathematically, a permutation (the formula being slightly different) treats these two hands as distinct. "Order unimportant" versus "order important" is a good way to describe this.

52p5 = 52!/(52-5)!, a much larger number than 52c5 ... 52!/[(5!)(52-5)!]

But yes - "n" and "r" are the variables; "c" and "C" are not different in the examples above.

End of lesson .... cease transmission

:::Loon puts his mathematics degree back in the dusty box:::