Is this related to Number Theory?

Probability Level 3

Suppose, you are making five digit numbers by only using the numbers 1, 2, 3, 4, 5 without repetition. What is the value of the sum of all of this numbers?


The answer is 3999960.

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Mahtab Hossain by Mahtab Hossain , 28, Bangladesh

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4 solutions

Sam Cheung
May 29, 2015

There is no "highest". There is only one solution. If you add all the possible five digit combinations you get 3999960.

For each possibility for each digit, there are 4! combinations, e.g. there are 4! five digit numbers starting with 5 (e.g. 54321, 53421, etc..).

This means that when we add up the possible digits in each place we get 5x4!+4x4!+3x4!+2x4!+1x4! = 360.

Times this by 11111 for each of the digits to get the total. 360x11111 = 3999960.

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Moderator note:

Yes, this is the standard approach.

Jaka Ong
May 29, 2015

(11111+22222+33333+44444+55555)×24 = 3999960

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Moderator note:

Why? How did you form that equation? Where is your reasoning?

The number 12345 We can change to 10000 + 2000 + 300 + 40 + 5 The number 12354 Can change to 10000 + 2000 + 300 + 50 + 4 And so on Until the number 54321 50000 + 4000 + 300 + 20 + 1

By filling slots we can know that each number in each position will have to appear for 24 times Example : * *5 (last digit five) 4 × 3 ×2 ×1 =24 Sorry if I text it amateurly.

Jaka Ong - 6 years ago
Shashank Rustagi
Mar 27, 2016

the solution is in the picture

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James Guevara
Jun 1, 2015

Get the sum of the lowest possible number which is 12345 and the highest which is 54321 then divide it by 2 to find its average which is 33333. In getting the sum of all its numbers first you must find all possible numbers which is 5! or 120 then multiply 33333 to 120 and you get the final answer which is 3999960!!!

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