Logic behind the number of combinations of numbers

Click For Summary
SUMMARY

The discussion focuses on calculating the total number of combinations for a 4-digit code using digits 0-9. Each digit has 10 possible choices, leading to a total of 10 x 10 x 10 x 10, which equals 10,000 combinations. The reasoning behind multiplication rather than addition is clarified through the explanation of choices available for each digit. Visualizing the combinations as a tree diagram is suggested to enhance understanding of the concept.

PREREQUISITES
  • Understanding of basic combinatorial principles
  • Familiarity with multiplication and addition in mathematical contexts
  • Knowledge of digit representation (0-9) in numerical systems
  • Ability to visualize data structures, such as tree diagrams
NEXT STEPS
  • Research combinatorial mathematics and its applications
  • Learn about permutations and combinations in mathematics
  • Explore tree diagrams for visualizing mathematical problems
  • Study the principles of counting in discrete mathematics
USEFUL FOR

Students, educators, mathematicians, and anyone interested in understanding combinatorial calculations and their applications in coding and security systems.

lntz
Messages
53
Reaction score
0
Hey,

so i think this is a fairly simple question but i'd like to get it firmly understood in my head.

How do you figure out the amount of combinations of digits in say a 4 digit code. with numbers 0-9...

I can't think of a good way to say it, but for example you could have 0,1,2,3 or 1,2,3,0 etc etc.

So how do you figure out quickly just how many combinations exist.


Thanks for any help you give
 
Physics news on Phys.org
Ten choices for the first number, ten choices for the second number...: 10 x 10 x 10 x 10 = 10,000

All of the numbers between 0000 and 9999.
 
Sorry my maths is lacking... why do you multiply the numbers, and not add them.
 
0 thru 9, or 10 different choices, for each digit.

00, 01, 02, 03...09 10 choices
10, 11, 12, 13...19 10 choices
20, 21, 22, 23...29 10 choices
...
30 thru 89... 60 choices
...
90, 91, 92, 93...99 10 choices
total 100 choices

000,001,002...099 100 choices
100,101,102...199 100 choices
...
200,201,202...899 700 choices
...
900,901,902...999 100 choices
total= 1000 choices

Do the same thing for the next digit...
 
It might help to imagine a tree diagram, with all the possibilities the numbers could be.
 

Similar threads

High School Two interesting number theory tricks
  • · Replies 3 ·
Replies
3
Views
998
MHB Game Night : Number of combinations
  • · Replies 14 ·
Replies
14
Views
2K
High School Combinatorics and Magic squares
  • · Replies 2 ·
Replies
2
Views
2K
High School I have an issue with Cantor's diagonal argument
  • · Replies 6 ·
Replies
6
Views
2K
High School Logic Problem: Figuring Out How Many Apples Each Man Ate
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad On the meaning of logical implication within specific context/models
  • · Replies 22 ·
Replies
22
Views
3K
High School Traditional logic and its usefulness in the past
  • · Replies 21 ·
Replies
21
Views
3K
High School Maximize Your Odds: Choosing Winning Lotto Combinations from 1 to 58
  • · Replies 15 ·
Replies
15
Views
5K
High School The number of possible combinations with a constraint
  • · Replies 2 ·
Replies
2
Views
2K
How many combinations? (High school math problem)
  • · Replies 20 ·
Replies
20
Views
2K