#6
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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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