Numbers formed by taking each of the digits 2,3,5,6 and 8 once?

17,534
7,134
What is the sum of all the numbers formed by taking each of the digits 2,3,5,6 and 8 once?
 

BoulderHead

haha, maybe later.
 

jamesrc

Science Advisor
Gold Member
476
1
6399936
 
32
0
Hmm...combinatorics.

2 3 5 6 8

There are: (5)*(5-1)*(5-2)*(5-3)*(5-4) or 5*4*3*2*1 = 120 permutations for the above set of numbers.

One set of numbers add up to: 2+3+5+6+8 = 24.

So, the sum of all numbers formed from 120 permutations is:

120*24 = 2880.
 

jamesrc

Science Advisor
Gold Member
476
1
If I answered the right question, for all of the 5-digit numbers you can make, each digit appears 24 times in each column, so you can write:

24*(22222+33333+55555+66666+88888)=6399936

Edit: Oh, I thought it was the sum of the numbers made by the combinations, not the sum of their digits.
 
Last edited:
17,534
7,134
Originally posted by jamesrc
If I answered the right question, for all of the 5-digit numbers you can make, each digit appears 24 times in each column, so you can write:

24*(22222+33333+55555+66666+88888)=6399936

Edit: Oh, I thought it was the sum of the numbers made by the combinations, not the sum of their digits.
James gets the point!

Here is an alternative way:
4!*(2+3+5+6+8)*(11111) = 6,399,936
 

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