Question

How many numbers less than 10000 can be made using the digits 1 2 3 4 5 6 7 0 digits can be repeated?

Answer 1

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.