Factorial Question

Quote: "The horrible Combination formula bit: n items can be chosen r ways at a time:

n! / {(n-r)! * r!}

For 2 card starting hands, this is calculated as:

52! / (50! * 2!)

(! is read as "factorial" where 6! = 6*5*4*3*2*1 and 3! = 3*2*1)

From the above, although it looks frightening to start with, you will quickly realise that through cancelling you can quickly arrive at (52 * 51) / 2 = 1326 possible hands, each with an equal chance of occurring."

Question (sort of): I do not quickly see how he cancels 52! / (50! * 2!) to arrive at (52 * 51) / 2. Any help here would be appreciated since I look suspiciously at 52!/(50!*2!) but laud (52*51)/2.

I realise calculus is a prerequisite for probability theory. I have already ordered PROBABILITY WITHOUT TEARS by Rowntree and although the book is supposedly designed for the mathematically handicapped <raises*hand!/sigh!*2!> I am googling for calculus, pre-calculus, and yes, pre-pre-calculus texts. Binomial coefficients, here I come.

Still, I was pretty good at cancelling out so if you think you can explain in 3k words or more, or less, do not hesitate! Thank you in advance if you are bold enough.

[BruceZ]

[ QUOTE ]
Question (sort of): I do not quickly see how he cancels 52! / (50! * 2!) to arrive at (52 * 51) / 2. Any help here would be appreciated since I look suspiciously at 52!/(50!*2!) but laud (52*51)/2.

[/ QUOTE ]

52!/(50!*2!) =

(52*51*<font color="red">50*49*48*....*1</font>) / [(<font color="red">50*49*48*...*1</font>)*(2*1)] = 52*51/2.

Note that everything in red cancels.

Think of this as "52 ways to pick the first card, times 51 ways to pick the second card, divided by 2 since we don't care about the order".

Why that tricky... Thanks BruceZ. I see I forgot how to cancel, and I have never cancelled that large a string of numbers before &lt;blushes&gt;. But yes, now it looks simple. I needed to expand /images/graemlins/smile.gif

Thank you for keeping it under 3k words.