Question 816250: How many 4 digit numbers can be formed if repetition is not allowed from the digits 0 to 9 ?
What's wrong with my answer: 6*8*9*10(10 for units, 9 for tens, 8 for hundreds,6 for thousand if zero was not taken)+ 7*8*9*10 (10 for units, 9 for tens ,8 for hundreds, 7 for thousand if zero was taken) =9360
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! You have it backwards
9*9*8*7=4536
9 for thousands - no zero
9 for hundreds -what ever was in the thousands can't be used
8 for ten because what ever was in thousands and hundreds can't be used
7 for units
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website! How many 4 digit numbers can be formed if repetition is not allowed from the
digits 0 to 9 ?
What's wrong with my answer: 6*8*9*10(10 for units, 9 for tens, 8 for
hundreds,6 for thousand if zero was not taken)+ 7*8*9*10 (10 for units, 9 for
tens ,8 for hundreds, 7 for thousand if zero was taken) = 9360
"6*8*9*10(10 for units, 9 for tens, 8 for hundreds, 6 for thousand if zero was
not taken)" allows for zero to be taken as the units digit.
The rule that must be followed is:
OF THE THINGS TO CHOOSE, ALWAYS CHOOSE THE MOST RESTRICTIVE THING FIRST.
In this case the most restrictive thing to choose is the first digit,
since it cannot be 0.
So we can choose the thousands digit 9 ways, leaving 9 ways for the hundreds,
8 for the tens, and 7 for the units or 9·9·8·7 = 4536.
Edwin
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