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How many integers between 1000 and 9999 have four distinct digits?

 Oct 25, 2019
 #1
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9 x 9 x 8 x 7 =4,536 such numbers.

 Oct 26, 2019
 #2
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Just an explanation of guest's answer

 

 

You have four digits

 

_   _   _   _
 

The first digit has 9 choices, because it can't be 0. So 1 through 9 will be 9 choices.

 

The second will also be 9 choices. This is because it now can include 0 but also excludes the previous digit.

 

The third digit has 8 choices, because it excludes the previous 2 digits.

 

The fourth digit has 7 choices, because it excludes the previous 3 digits.

 

So 9 * 9 * 8 * 7 = 4536

CalculatorUser  Oct 26, 2019

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