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There is a six-digit number, where each digit is either a 1, 2, or 3. If no two consecutive digits are 1, how many of these six-digit numbers are there?

 Sep 6, 2020
 #1
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Hint: Use complementary counting! What is the total number of possibilities – the ones that have two consecutive digits of one?

 

Hint 2: There are \(3^6=729\) total possibilities. What do you need to subtract?

 

Hope this helps!

 Sep 6, 2020

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