Solving Combinatorics: Finding the Number of Sets with Elements from A, B, and C

In summary, Combinatorics is a branch of mathematics that involves counting, arranging, and selecting objects according to certain rules. It has various applications in fields such as computer science, statistics, economics, and chemistry. Common techniques used in Combinatorics include permutations, combinations, and the use of binomial coefficients. Permutations involve arranging objects where order matters, while combinations involve selecting objects where order does not matter. To improve understanding of Combinatorics, one can practice problems, read textbooks or online resources, and seek help from a tutor or mentor.
  • #1
Neitrino
137
0
Please help me with combinatorics:
I have three sets:
A with elements (a1 ……..ai )
B with elements (b1 ……..bk )
C with elements (c1 ……..cj )

Pls help me to work out how many sets ABC shall I have that contain each element from sets A, B and C

Thanks much
 
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  • #2
You can try to simplify the problem first by considering something you can do by simple enumeration with A (a1,a2) B(b1,b2) and C(c1,c2). Then you try to generalize your results. Of course there are better ways, fancier etc but at least you have a starting point.
 

1. What is Combinatorics?

Combinatorics is a branch of mathematics that deals with counting, arranging, and selecting objects or elements according to certain rules or principles.

2. How is Combinatorics applied in real life?

Combinatorics is used in various fields such as computer science, statistics, economics, and chemistry. It can be applied in data analysis, probability calculations, and optimization problems.

3. What are some common techniques used in Combinatorics?

Some common techniques used in Combinatorics include permutations, combinations, and the use of binomial coefficients.

4. What is the difference between permutations and combinations?

Permutations are arrangements of a set of objects where order matters, while combinations are selections of objects where order does not matter.

5. How can I improve my understanding of Combinatorics?

Some ways to improve your understanding of Combinatorics include practicing problems, reading textbooks or online resources, and seeking help from a tutor or mentor.

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