SOLUTION: how many numbers greater than 500000 can be made from digits 2,3,4,5,6,and 7 without repeatition if the number is odd?

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Question 957528: how many numbers greater than 500000 can be made from digits 2,3,4,5,6,and 7 without repeatition if the number is odd?
Answer by Edwin McCravy(20063)   (Show Source): You can put this solution on YOUR website!
Two case:

Case 1: The 6th (last) digit is 3

Choose the 6th digit 1 way, {3}
Choose the 1st digit any of 3 ways, {5,6,7}
Choose the 2nd digit any of the remaining 4 digits
Choose the 3rd digit any of the remaining 3 digits
Choose the 4th digit either of the remaining 2 digits  
Choose the 5th digit as the 1 remaining digit.

That's 1*3*4*3*2*1 = 72 ways

====================

Case 2: The 6th (last) digit is 5 or 7

Choose the 6th digit 2 ways, {5,7}
Choose the 1st digit either of 2 ways, {whichever two of {5,6,7} that remain.
Choose the 2nd digit any of the remaining 4 digits
Choose the 3rd digit any of the remaining 3 digits
Choose the 4th digit either of the remaining 2 digits  
Choose the 5th digit as the 1 remaining digit.

That's 2*2*4*3*2*1 = 96 ways

================

Total for the two cases = 72 + 96 = 168

Edwin
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