Formula for How Many Combinations We Can Have From Two Sets with Restrictions

Formula for How many combinations we can have from two sets with restrictions

Formula for How Many Combinations We Can Have From Two Sets with Restrictions 1

If I understand correctly, you can solve this as a set packing problem. For $Ssubset 1,dots,50$ with $|S cap A|=5$ and $|S cap B|=2$, let binary variable $x_S$ indicate whether set $S$ is selected. The problem is to maximize $sum_S x_S$ subject to: $$sum_S: i,j subset S x_S le 1 quad textfor $1le i

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Two sets can be separated by a hyperplane iff their convex hulls do not intersect

Following dtldarek's answer above: Let the unit normal vector for the plane $P$ be $n=dfrac(p_0-p_1)lVert p_0-p_1

Vert$. Then for any $xin C_1$, $n^

m T(x-p_0)m T(y-p_0)>dfracd2>0$. So $n^

m Tx-n^

m Tp_0 m Ty-n^

m Tp_0>0$.This shows that the points in $C_1$ and $C_2$ are linearly separable

Formula for How Many Combinations We Can Have From Two Sets with Restrictions 2

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Two sets of labels on pgfplot bar chart

The following works for two data series. The idea is to add two labels below each x value, one to the left (anchor=east) and one to the right (anchor=west). The x position is taken from the symbolic x coordinates system, the y coordinate is taken from the xticklabel cs, which lies on the x axis. If we would just put the corresponding

ode command into the axis environment, it would be clipped away. The option after end axis/.code allows to specify code to be executed after the clipping.EDIT: Labels above x axisI overread that you wanted to have the labels above the xaxis. This can be achieved with the following change to the above code:

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Notation Help: Set of pairings of items from two sets

Using the idea from a comment of halrankard2 (formerly halrankard) combined with the thoughts in the OP, I believe the desired $C$ could be written: $$C=left left left.left a,f(a)


ight| ainalpha

ight left|alphainbinomAminleft(|A|,|B|

ight) ,f:alphato Btext injective


ight$$To condense this even more, note that "$f:alphato Btext injective$" might be written "$f:alphahookrightarrow B$" in some texts.Also, note that the $binomAk$ notation is not very common, so it should probably be explained first.This is such a weird operation (in part because it combines the qualitatively different $|A||B|$ cases) that I would not recommend writing the above without providing an example or two. It's so complicated that I would not recommend writing the above at all, and instead breaking it down into steps. Depending on the application, pseudocode resembling the Python might be preferable to math notation entirely.

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Why does the Boeing 777X airliner only have two sets of rear landing gear even though it has a higher maximum takeoff weight than early versions of the Boeing 747 jumbo jet that had 4 sets of rear landing gear?

The 747 arrived in 1970: prehistory.Steam trains were running in India then.Runways and taxiways were not built to take large loads; they had low LCNs.The 777 arrived in 1995: a full 25 years later.Even South Sudan could build good runways and taxiways by then. The 777 has 12 main wheels to take the load of the airplane compared to the 747's 16; in 25 years, enough runways and taxiways have been strengthened to make this possible

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Should there be two sets of codes on a LV Batignolles Horizontal Monogram Bag?

i do not know those details- sorry, but... BUYER BEWARE Spotting a knockoff is more difficult than you might think. Arm yourself with these key information points to avoid purchasing a fake. Location, Location, Location First and foremost, purchasing luxury goods at a brand's boutique, Web site or authorized dealer is your best bet to insure buying a genuine product. Items at flea markets, home parties, from street vendors or unauthorized Web sites are likely to be fake. The Price is Right Quality and exclusivity account for the high price of luxury goods. So, if the price seems too good to be true, it probably is. Construction Sites Craftsmanship is a main point of distinction with luxury goods. Sloppy stitches in less visible areas - such as the underside of a product or inside pockets - is likely the result of counterfeit production. Package Deal Luxury retailers meticulously package their products, including tissue paper, authenticity cards, product care information, and superior quality boxes and shopping bags. If you see a plastic wrap covering or a flimsy dust bag, it's probably a fake. For example, counterfeit manufacturers will often wrap the handles of handbags in plastic. Spellcheck Counterfeiters will often misspell designer names. Check for letters that are swapped or a letter that is capitalized that should not be, and vice versa. Check the Hardware With most luxury accessories, you will find the logo on all the metal pieces, such as zippers, latches, snaps and buckles. Read the Label In a genuine article of luxury clothing, most often the label is stitched in, whereas counterfeit clothes are likely to have a less expensive hangtag. Also check the country of origin on the label. Timely Tips Makers of fake watches may not replicate unusual features, such as a helium relief valve. If the feature is available, often times it does not function.

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