SOLUTION: How many 5-digit numbers have at least one zero?

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Question 390865: How many 5-digit numbers have at least one zero?
Found 2 solutions by richard1234, solver91311:
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
First, find the total number of 5-digit numbers:

9*10*10*10*10 = 90000 (10 digits for each placeholder except the first)

Then, find the number of 5-digit numbers with *no* zeros (so that we can subtract from 90000 and find the number of 5-digit numbers with at least one 0):

9*9*9*9*9 = 59049 (9 digits for each placeholder)

90000 - 59049 = 30951.


Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


The smallest 5 digit number is 10000. The largest is 99999. 99999 minus 10000 is 89999, but since you have a zero-based count, you have to add 1. That means there are a total of 90000 different 5 digit numbers.

If you disallow zeros in all 5 digits, there are 9 ways to choose the first digit, 9 ways to choose the 2nd digit, and so on so there are 5 digit numbers that have no zeros at all.

Hence the difference between 90000 and 59049 is the number of 5 digit numbers with at least one zero.

John

My calculator said it, I believe it, that settles it
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