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iComb - Interactive Combinatory on the Internet

The iComb - Interactive Combinatory on the Internet is a free system for teaching and learning topics associated with combinatory and can be used in the Web. The iComb is one of the e-learning module(✮) freely available from the iMática project.
The iComb is based on Combien?, a system developed by the Université Pierre et Marie Curie (LIP6), which can not be directly integrated to Web browsers. It can also be used as a widget that can help students to learn how to solve combinatoric exercises and understand their related concepts. A widget is a mini-application that can be easily added to Web sites by using the copy-and-paste pattern. The use of iComb is inspired by the idea of bringing up mathematical domains to the changing trend named as Web 2.0 and encouraging the development of a family of "math widgets" to improve the mathematical education scenario To try now, just copy the piece of code below to your blog or web page.

iComb Widget!

Copy the code above and add iComb in your Web page!


Exercise 1

With a 32-card pack, how many two-card hands is it possible to form with exactly 1 queen and exactly 1 ace?

Exercise 2

With a 32-card pack, how many five-card hands is it possible to form with exactly 2 hearts and exactly 2 spades?

Exercise 3

With a 52-card pack, how many eight-card hands is it possible to form with exactly 1 ace, 2 kings and 2 jacks?

Exercise 4

With a 32-card pack, how many eight-card hands is it possible to form with exactly 4 aces and 4 kings?

Exercise 5                                         

With a 32-card pack, how many twenty-card hands is it possible to form with 3 aces, 4 spades and 16 reds?

Exercise 6

With a 32-card pack, how many twelve-card hands is it possible to form with at least seven hearts, exactly 4 aces, 2 spades and nothing else?

Exercise 7

With a 32-card pack, how many eighteen-card hands is it possible to form with 6 diamonds, at most 4 blacks, exactly 4 jacks and exactly 4 aces?

Exercise 8

With a 32-card pack, how many thirteen-card hands is it possible to form with at least 1 hearts, exactly 4 blacks and exactly 4 aces?

Exercise 9

With a 32-card pack, how many thirteen-card hands is it possible to form with 12 reds, exactly 3 aces and at most 4 diamonds?

Exercise 10

How many 13 players team can form with just 5 teammates in blue and just 5 players on the team green?