How many nine-digit numbers meet these criteria?

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In summary, combinatorics is a branch of mathematics that deals with counting and arranging objects or elements in a finite or discrete manner. Its fundamental principles include the multiplication principle, addition principle, and the principle of inclusion and exclusion. Combinatorics has various applications in fields such as computer science, statistics, physics, and biology, and is used in designing algorithms, analyzing network structures, and studying genetics. The difference between permutation and combination is that permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without considering their order. Combinatorics plays a crucial role in everyday life, from arranging items in a store to designing schedules and creating passwords, and also helps in making decisions based on probabilities
  • #1
stamenkovoca02
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The number of nine-digit numbers divisible by 225 in which all digits are different and in which the digit of hundred is 7 is?
I don't know how to set the number to be divisible by 225, so if anyone can help
 
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  • #2
255= 3(5)(17) so any number divisible by 255 must be divisible by 3, 5, and by 17. Any number divisible by 3 has digits that sum to a multiple of 3. Any number divisible by 5 has one's place 5 or 0. 17 is the hard one!
 

FAQ: How many nine-digit numbers meet these criteria?

What is combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging objects in a systematic way.

What are the main areas of combinatorics?

The main areas of combinatorics include enumeration, graph theory, design theory, and combinatorial geometry.

How is combinatorics used in real life?

Combinatorics has many applications in real life, such as in computer science, cryptography, genetics, and game theory.

What are some common combinatorial problems?

Some common combinatorial problems include the binomial theorem, permutations and combinations, and the pigeonhole principle.

What skills are needed to be successful in combinatorics?

To be successful in combinatorics, one needs a strong understanding of basic mathematics, logical thinking, and problem-solving skills.

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