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Old 12-31-2005, 06:40 AM
Mike Haven Mike Haven is offline
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Join Date: Sep 2002
Location: Northern Ireland
Posts: 2,288
Default Re: probability of getting flush with suited hand

For anyone who can't remember why, for example,
C(11,3)*C(39,2) should equal 122,265 this might help:

C(n,r) is often written as nCr

and it equals (n!)/[(n-r)!r!]

(note: n! is spoken as "n factorial" and means multiplying all the numbers from 1 up to n together; so if n = 4, n factorial would mean 1*2*3*4 or 1x2x3x4 or 4x3x2x1 or 24)

which for 11C3 means (11x10x9x8x7x6x5x4x3x2x1)/[(11-3)!3!]

or (11x10x9x8x7x6x5x4x3x2x1)/(8x7x6x5x4x3x2x1)x(3x2x1)

(note: you can simply cross off the (8x7x6x5x4x3x2x1) from the end of the (11x10x9x8x7x6x5x4x3x2x1) without having to multiply them both out, which will give

or (11x10x9)/(3x2x1)

or 165

and for 39C2 means (39x38x...)/[(39-2)!2!]

or (39x38x...)/[(37x36x...)x(2x1)]

or (39x38)/(2x1)

or 741

so 11C3*39C2

or C(11,3)*C(39,2)

or C(11,3) x C(39,2)

or 165 x 741

equals 122,265.

I hope is useful to someone, and if you save these calculations they might make the next combinations thread a little easier to understand.
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