SOLUTION: How many numbers less than 10000 can be made with the eight digits 1,2,3,0,4,5,6,7

Question 293969: How many numbers less than 10000 can be made with the eight digits 1,2,3,0,4,5,6,7
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!


All numbers with 4 or fewer digits will be less than 10000

1-digit numbers:
There are 8 1-digit numbers 1,2,3,0,4,5,6,7

2-digit numbers
Choose 1st digit 7 ways (not 0), then choose 2nd digit 7 ways
7*7 or 49 2-digit numbers

3-digit numbers
Choose 1st digit 7 ways (not 0), then choose 2nd digit 7 ways,
then 3rd digit 6 ways
7*7*6 or 294 3-digit numbers

4-digit numbers
Choose 1st digit 7 ways (not 0), then choose 2nd digit 7 ways,
then 3rd digit 6 ways, and finally 4th digit 5 ways
7*7*6*5 or 1470 4-digit numbers

Answer 8 + 7*7 + 7*7*6 + 7*7*6*5 = 8 + 49 + 294 + 1470 = 1821.

Edwin

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