Asked Sep 25, 2019

How many integers greater than 5400 and less than 10000 have both of the following properties:

- digits are distinct

- digits 2 and 7 do not occur.

I got that there are 1680 integers from 0-9999 and 960 integers from 0-5400 with those two properties so using the subtraction principle then there are 720 from 5401-9999 with those two properties.


Expert Answer

Step 1

To count the number of positive integers satisfying all the required properties

Step 2

So, we are looking for filling 4 blank spaces satisfying all these condtions.


Image Transcriptionclose

5400 ; <x<10000 digits are distinct; 2,7 should not occir

Step 3

First blank (leftmost digit) can only be filled in 4 ways (5,6,8,9), second in 4 ways. as 4 is also a candidate.  The remain...


Image Transcriptionclose

5400 x <10000; digits are distinct; 2,7 should not occur


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