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Can someone give me a hand with understanding the formula behind this better?
I can't seem to wrap my head around it?
How many odd three-digit integers greater than 800 are there such that all their digits are different?
(C) 2008 GMAT Club - m25#20
40 56 72 81 104 If the number begins with 8, there are possibilities (5 possibilities for the last digit and 8 possibilities for the middle digit). If the number begins with 9, there are possibilities (4 possibilities for the last digit and 8 possibilities for the middle digit). In all, there are numbers that satisfy the constraints.
Number of odd digit numbers starting with 8. Hundreds place is filled with 8. For a number to be odd, units place should be filled with either 1, 3, 5, 7, 9. So there are 5 possibilities. Tens place can be filled with either 0,1,2,3,4,5,6,7,9 . But we have to eliminate the digits that are used in units position. So number of odd numbers with unique digits starting with 8 = 1*8*5 = 40 ways.
For numbers starting with 9, unit digit can be either or 1,3,5,7 So number of odd numbers with unique digits starting with 9 = 1*8*4 = 32 ways.
So total number of possible combinations = 40 + 32 = 72 ways