User:Marc van Leeuwen/sandbox

One

Just testing math ${\mathfrak {g}}$, x² = 5y − i x⁄y

Underlined exponents

I have commented it out. Go ahead and restore my last edit if it is mathematically meaningful.

${\frac {52^{\underline {5}}}{5!}}$

AAS 16:42, 27 March 2011 (UTC) — Preceding unsigned comment added by Ann arbor street (talk • contribs)

Okay, from what was explained to me, this is falling factorial power notation. I haven't heard of it before and I am not sure how approriate it is in this article, so I'll copy the text I commented out here for discussion and or somebody just reverting me.

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As a concrete example, one can compute the number of five-card hands possible from a standard fifty-two card deck as:

${52 \choose 5}={\frac {52^{\underline {5}}}{5!}}={\frac {52\times 51\times 50\times 49\times 48}{5\times 4\times 3\times 2\times 1}}={\frac {311,875,200}{120}}=2,598,960.$

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That's it. Ann arbor street (talk) 22:29, 27 March 2011 (UTC)

I've tried to restore the section into a coherent state that retains the new example with an explanation, and to put in an indication with wikilink where the falling factorial power notation is first used. Marc van Leeuwen (talk) 07:54, 28 March 2011 (UTC)

Just one more point: read the section #Efficient computation above to see why it is useful to give

Three

see section #two above

[[Category::Combinatorics]]