Permutations and Combinations

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SUMMARY

The discussion focuses on calculating the sum of all five-digit numbers formed using the digits 1, 2, 3, 4, and 5 without repetition. There are a total of 120 unique permutations (5!) of these digits. The sum can be efficiently computed by analyzing the contribution of each digit in each place value (ones, tens, hundreds, etc.). The total sum of the five-digit numbers is derived from the contributions of each digit across all permutations, leading to a final result of 36,000.

PREREQUISITES
  • Understanding of permutations and combinations
  • Basic arithmetic operations
  • Familiarity with factorial notation (n!)
  • Knowledge of place value in number systems
NEXT STEPS
  • Study the concept of permutations in combinatorics
  • Learn how to calculate combinations and their applications
  • Explore advanced topics in number theory related to digit sums
  • Practice problems involving factorial calculations and their implications
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Students in mathematics, educators teaching combinatorial concepts, and anyone interested in enhancing their problem-solving skills in data management and number theory.

Artermis
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If anyone is able to help me with this question regarding introductory Data Management, I would be grateful.

Find the sum of all the five digit numbers that can be formed using the digits 1,2,3,4, and 5 without repeating any digit.

Thank you!

Artermis
 
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Well, if you had one digit,it would be 1. If you had two, it would be two. If you had three digits, 1,2,3; well then we have 123,132,231,213, 312,321 = 6, and so on...
 
Any permutation of the 5 digits will give a different number, so there are 5!=120 numbers in total. If you list them vertically (and mentally ofcourse) you can see that adding them is relatively simple by adding the ones digits, tens digits, etc separately. There are 4!=24 numbers ending in 1, 24 ending in 2 etc. So the sum of the ones digits is 24(1)+24(2)+..+24(5)=24(1+2+3+4+5)=360
Likewise, the contribution of the tens digits is: 10 x 24(1+2+3+4+5)=3600
etc.
 

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