How many 3 digit numbers can you make from the digits 0,1,2,3,4,5,6 if the 3 digits must greater than 500 and repetition is not allowed?

They must start with either the 5 or the 6.

Consider those that start with a 5.  

There are 6 digits left that could go in the "tens" position.

 For each of these there are 5 digits left that could go in the "units" position.

 Hence there are 6*5 = 30 possible 3-digit numbers beginning with 5.  

 

Similar reasoning shows that there are also 30 possible 3-digit numbers beginning with 6.

 

So there are 60 possibilities in all.

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