SOLUTION: How many 3-number combinations might a student have to try in order to open a lock if the numbers from 0 to 39 appear on the dial? Assume that the second number may be the same as

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Question 926887: How many 3-number combinations might a student have to try in order to open a lock if the numbers from 0 to 39 appear on the dial? Assume that the second number may be the same as the first (since the dial will be rotated in a different direction), but the third number must be at least 5 away from the second.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
There are 40 ways to choose the first number
and there are 40 ways to choose the second number.

Now we take some examples to determine how many choices there are for 
the third number 

If the second number is 23, then the 3rd number cannot be any of these
9 numbers 19,20,21,22,23,24,25,26,or 27, since they are not at least 5 
numbers away from 23.  Same for all other 40 second numbers. 

Let's look at a second example which includes some on both sides of 0.
If second number is 2, we couldn't choose any of the 9 numbers 38,39,0,1,2,3,4,5,6.

So thats 40-9 or 31 choices for the 3rd number.

Answer 40*40*31 = 49600 ways.

Edwin