SOLUTION: How many ways to make a 3 digit number by using numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 That is divisible by 10

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Question 974945: How many ways to make a 3 digit number by using numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
That is divisible by 10
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Edwin is incorrect.
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You didn't say if odd an even numbers had to alternate - he didn't solve for that.
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Edwin is actually my mother-in-law.
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How many ways to make a 3 digit number by using numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
That is divisible by 10
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The 1's digit has to be zero.
If, eg, 010 is not considered to be a 3 digit #, then the 1st digit cannot be zero.
--> 9*10*1 = 90 ways.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
The other tutor's solution is incorrect.

You didn't say whether we can repeat digits or not.

If we can repeat the digits, then:

Choose the last digit 1 way as 0.
Choose the first digit any of 9 ways (can't use 0)
Choose the middle digit any of 10 ways (can use 0).

That's 1*9*10 = 90 3 digit numbers divisible by 10, assuming digits can be
repeated, such as 100, 990, etc.

Answer: 90

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If we cannot repeat the digits, then:

Choose the last digit 1 way as 0.
Choose the first digit any of 9 ways 
Choose the middle digit any of 8 ways

That's 1*9*8 = 72 3 digit numbers assuming digits cannot be repeated.
 
Answer: 72

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Edwin
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