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How many 4 -digit positive integers have 2 or more zeroes?

 Jul 5, 2020
 #1
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My computer says there are =252 such numbers. Somebody will confirm it by using combinations such as:

9 nCr 3 * 3 =252  or  maybe: (10 nCr 4 - 9 nCr 3) *2 =252......etc.

 Jul 5, 2020
 #2
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case 1: there are 3 zeros.

 - This one is pretty trivial, we know there are 9 of these numbers (1000, 2000, 3000... 8000, 9000)

 

case 2: there are 2 zeroes.

 - All we need to do is find the number of such cases for the 1000s and multiply that for 9.

 

1001, 1002... 1008, 1009 there are 9 cases for which the the single digit is not zero

 

1010, 1020, ... 1080, 1090 there are 9 cases also.

 

Obviously there are also 9 cases for the non-zero hundreds digit cases.

 

So there are (9 + 9 + 9) * 9 = 243 for case 2.

 

 

So case 1 + case 2 = 252 such numbers, confirming guest's answer

 Jul 5, 2020

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