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FInd the number of 4-digit numbers, where each digit is 0, 1, or 3.

 Aug 4, 2020
 #1
avatar+28021 
+1

I will assume there cannot be a 0 in the first position

 

2 choices for first digit

3 choices for 2nd

3 choices for 3rd

3 choices for 4th

 

2  x  3  x  3  x  3 =....... choices

 Aug 4, 2020
 #2
avatar+169 
+1

Let's See:

 

For each digit space, there can be any number, with the exception that the 1000s place cannot have a 0. We have 2 choices for the thousands place, either 1 or 3.

 

For the 100s place, any number is okay. 0,1, and 3 all work just fine

 

For the 10s place, any number can be there as well

 

For the 1s place, it's still 3 choices

 

So we have 2 choices, 3, choices, 3 choices, and 3 choices. What now? Well, we multiply our answers together, just how you would do a "clothes combination" problem. I will let you do the multiplication for yourself.

 Aug 4, 2020

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