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The number of subsets of size r that can be selected from a set of n elements is n denoted as 1 n 2 or Cr and r n a b r n! r!1n r2! (S2-4)

Pixel shaders can be applied to display objects with the ShaderFilter class. This lter consumes a Shader object, set in the constructor or assigned to its shader property, and runs the shader, setting its rst input to the display object it is ltering. Thus, your shader kernel must accept at least one image4 input.

EXAMPLE S2-5

Shaders give you full programmatic control over the pixels on-screen. If you have an effect in mind that you can t achieve with any of Flash Player s built-in lters, you can write a custom shader for the effect. Likewise, you can replicate any of the lters covered in this chapter with a shader. Shaders are covered in detail in 38.

A printed circuit board has eight different locations in which a component can be placed. If ve identical components are to be placed on the board, how many different designs are possible Each design is a subset of the eight locations that are to contain the components. From Equation S2-4, the number of possible designs is 8! 5! 3! 56

Summary

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The following example uses the multiplication rule in combination with Equation S2-4 to answer a more dif cult, but common, question. EXAMPLE S2-6 A bin of 50 manufactured parts contains three defective parts and 47 nondefective parts. A sample of six parts is selected from the 50 parts. Selected parts are not replaced. That is, each part can only be selected once and the sample is a subset of the 50 parts. How many different samples are there of size six that contain exactly two defective parts A subset containing exactly two defective parts can be formed by rst choosing the two defective parts from the three defective parts. Using Equation S2-4, this step can be completed in 3 a b 2 3! 2! 1! 3 different ways

Then, the second step is to select the remaining four parts from the 47 acceptable parts in the bin. The second step can be completed in a 47 b 4 47! 4! 43! 178,365 different ways

Filters let you apply bitmap effects to display objects. You can apply a lter to a display object by adding a BitmapFilter subclass to the filters array property that every DisplayObject possesses. Filter effects are cumulative and applied in the order they appear in the filters array. Filter objects are stored and retrieved by copy, so you must assign a new filters array to update the lters applied to a display object. Flash Player has a number of built-in lters that can be used for many purposes.

Therefore, from the multiplication rule, the number of subsets of size six that contain exactly two defective items is 3 178,365 535,095

ixel Bender, a cross-product toolkit for image processing, opens a whole new set of possibilities in Flash Player version 10 and above. You can use Pixel Bender to generate graphics, to lter display objects, to create custom blend modes, and even to process heaps of nonimage data. Pixel Bender uses its own language entirely separate from ActionScript 3.0, and it is compiled before being used in Flash Player. In this chapter, you ll learn about the ways Pixel Bender can enhance your Flash applications, how to load and use Pixel Bender programs in ActionScript, and how to program in the Pixel Bender kernel language.

to illustrate the use of the graphical interface for translating abstract syntax of the ATaG program into the concrete syntax used for software synthesis,

As an additional computation, the total number of different subsets of size six is found to be a 50 b 6 50! 6! 44! 15,890,700

FP10. Only Flash Player 10 and up can execute Pixel Bender kernels. Future versions of Flash Player may add support for Pixel Bender features not currently available, such as dependent values, region functions, loops, arrays, variable vector indices, and so on.

When probability is discussed in this chapter, the probability of an event is determined as the ratio of the number of outcomes in the event to the number of outcomes in the sample space (for equally likely outcomes). Therefore, the probability that a sample contains exactly two defective parts is 535,095 15,890,700 0.034

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