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

 May 28, 2023
 #1
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This is a computer code in C++:

 

d=0; if(d==0, goto Begin, goto End);

Begin:d=0;a=listfor(i,10000,99999,i);c=sumforeach(x, a, x%10==d or (x div 10)%10==d and x>9 or (x div 100)%10==d and x>99  or (x div 1000)%10==d and x>999 or (x div 10000)%10==d and x>9999;print"Total(0)=",c;return;

 

Total= 30,951 - this is the number of integers with at least 1 zero.

 May 28, 2023
 #2
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Algerba Help: 

https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.390865.html#:~:text=That%20means%20there%20are%20a%20total%20of%2090000,5%20digit%20numbers%20with%20at%20least%20one%20zero.

 

Gmatclub:

https://gmatclub.com/forum/how-many-5-digit-numbers-have-at-least-one-zero-digit-411268.html

 

Same question.

 

Overview:

(9*10*10*10*10)-9^5= 30951

Total 5 digit numbers-5 digit numbers without a 0=5 digit numbers with a 0

 

Answer is 30951

 May 28, 2023

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