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

• Greg Bernhardt
In summary, the sum of all numbers formed by taking each of the digits 2,3,5,6 and 8 once is 6,399,936. This can be calculated by finding all permutations of the numbers and then multiplying it by the sum of the digits. Alternatively, it can be calculated by multiplying the factorial of 4 (the number of digits) by the sum of the digits, and then multiplying that by 11111 (the number of possible combinations for each digit).
What is the sum of all the numbers formed by taking each of the digits 2,3,5,6 and 8 once?

haha, maybe later.

6399936

Originally posted by jamesrc
6399936

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.

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:
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

## 1. What is the largest possible number that can be formed using these digits?

The largest possible number that can be formed using these digits is 86532.

## 2. What is the smallest possible number that can be formed using these digits?

The smallest possible number that can be formed using these digits is 23568.

## 3. How many different numbers can be formed using these digits?

A total of 120 different numbers can be formed using these digits.

## 4. What is the sum of all the numbers that can be formed using these digits?

The sum of all the numbers that can be formed using these digits is 240,000.

## 5. Is there a pattern or rule for arranging these digits to form the largest possible number?

Yes, the digits should be arranged in descending order from left to right to form the largest possible number. In this case, it would be 8, 6, 5, 3, 2.

• General Discussion
Replies
16
Views
1K
• General Discussion
Replies
5
Views
2K
• General Discussion
Replies
10
Views
1K
• General Math
Replies
4
Views
191
• Math POTW for Secondary and High School Students
Replies
1
Views
836
• General Discussion
Replies
12
Views
1K
• General Math
Replies
23
Views
1K
• General Discussion
Replies
19
Views
2K
• General Discussion
Replies
13
Views
1K
• General Discussion
Replies
10
Views
2K