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How many positive integers less than 1000 have at least one digit of 0?

 

In how many ways can 45 cents be made using any combination of quarters, dimes, and nickels?

 May 9, 2021
 #1
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1. By complementary counting, there are 999 - 111 - 11 - 1 = 876 such positive integers.

 

2. There are 6 possible combinations.

 May 9, 2021
 #2
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1 - There are 180 integers with at least one "zero".

 

 

2 - There are 8 ways of making up 45:

       N  D  Q 

1  = 9   0   0
2  = 7   1   0
3  = 5   2   0
4  = 3   3   0
5  = 1   4   0
6  = 4   0   1
7  = 2   1   1
8  = 0  2   1

 May 9, 2021

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