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How many numbers between 200 and 700 have the property that all their digits are distinct?

 May 9, 2020
 #1
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There are 432 such  numbers.

 May 9, 2020
 #2
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1 - Start with the first digit from the left. You have 6 choices:2, 3, 4, 5, 6, 7

 

2 - Start with the 2nd digit from the left. You have 9 choices: 0, 1, 3, 4, 5, 6, 7, 8, 9 (when it begins with 2).

 

3 - Start with the 3rd digit from the left. You have 8 choices: they could be any of remaining 8 digits as long as they are different from the 1st and 2nd digits. if the 2nd is 3, then you have: 0, 1, 4, 5, 6, 7, 8, 9.

 

4 - So, the total number will be: 6 x 9 x 8 = 432 such numbers.

 May 9, 2020

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