How many nine-digit numbers meet these criteria?

  • MHB
  • Thread starter stamenkovoca02
  • Start date
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
4
0
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
 
Mathematics news on Phys.org
  • #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!
 

1. What is combinatorics?

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

2. What are the main areas of combinatorics?

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

3. How is combinatorics used in real life?

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

4. What are some common combinatorial problems?

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

5. 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.

Similar threads

I Leading digits of incomputable large numbers
    • General Math
Replies
11
Views
1K
MHB Solving Permutations Question with Restrictions
    • General Math
Replies
3
Views
814
B How to pick some numbers out of 13 integers, by a 4 digits code
    • General Math
Replies
4
Views
239
B How many numbers are there between 0 and 1
    • General Math
Replies
12
Views
3K
B Four Digit Numbers from 2x2 Digits - Simple Math Puzzle
    • General Math
Replies
20
Views
1K
MHB Probability: Find the number of ways to form 4-digit numbers >3000
    • General Math
Replies
4
Views
2K
MHB How can the sum of digits of a multiple of 2016 equal 2016?
    • General Math
Replies
6
Views
2K
MHB Recreational Number Theory, Unsolved Problem
    • General Math
Replies
1
Views
1K
I Is dealing with large numbers as formula a thing? and how is it done?
    • General Math
Replies
3
Views
1K
B Algorithm for checking if a set of digits are all distinct
    • General Math
Replies
25
Views
2K

Hot Threads

Recent Insights

Back
Top