Could you please help me with the following problem, How many different 4-digit numbers are there that use each of the digits 7,8,9,and 0? Please list them.

Thank-You
Ryan ( student,grade 4)

Hi Ryan,

Imagine that you have a small pad of paper and you are going to write one 4-digit number on each page from the pad. Tear of the first page and write 7 on it.

7      

If you now want to add a second digit you can add an 8, a 9 or a 0, so you need to take two more pages from the pad and write

7 8    
 
7 9    
 
7 0    

To add a third digit to any one of the pages you have two choices. For example the page that starts 78 you can extend to 789 or 780. So now you have

7 8 9  
 
7 8 0  
 
7 9 8  
 
7 9 0  
 
7 0 8  
 
7 0 9  

Finally for each of the six pages above you only have one digit that can be added. Thus the list so far is

7 8 9 0
 
7 8 0 9
 
7 9 8 0
 
7 9 0 8
 
7 0 8 9
 
7 0 9 8

This is the list of all 4-digit numbers that start with 7 and use each of the digits 7,8,9,and 0?

Now repeat this process but start with 8 rather than 7. Do it again, starting with 9 and finally do it starting with 0.

Cheers,
Penny
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