Question Number 51227 by mr W last updated on 25/Dec/18

Commented by mr W last updated on 25/Dec/18

Commented by Rasheed.Sindhi last updated on 26/Dec/18

Commented by mr W last updated on 26/Dec/18

Commented by Rasheed.Sindhi last updated on 27/Dec/18

Answered by Rasheed.Sindhi last updated on 26/Dec/18
![Case: Th=9 The biggest number is 9087 The smallest number 9013 th=9 (1 way) h=0(1 way) u={1,3,5,7,9}−{0,9}={1,3,5,7}(4 ways) t={0,1,2,3,4,5,6,7,8,9}−{0,9,u}(7 ways) ∴ Total ways(numbers) with 9 thousand 1×1×7×4=28 Case: Th=3,5,7 th={3,5,7}(3 ways) u={1,3,5,7,9}−{th}(4 ways) h={0,1,2,3,4,5,6,7,8,9}−{th,u}(8 ways) t={0,1,2,3,4,5,6,7,8,9}−{th,u,h}(7 ways) ∴ Total ways(numbers) 3×4×8×7=672 Case:Th=4,6,8 th={4,6,8}(3 ways) u={1,3,5,7,9}−{th}={1,3,5,7,9}(5 ways) h={0,1,2,3,4,5,6,7,8,9}−{th,u}(8 ways) t={0,1,2,3,4,5,6,7,8,9}−{th,u,h}(7 ways) ∴ Total ways(numbers) 3×5×8×7=840 Case: Th=2 2013 to 2987 th={2}(1 way) u={1,3,5,7,9}(5ways) h={0,1,2,3,4,5,6,7,8,9}−{2,u}(8 ways) t={0,1,2,3,4,5,6,7,8,9}−{2,u,h}(7 ways) ∴ Total ways(numbers) 1×5×8×7=280 Case: Th=2 ( up to 2019(exclusive) ) th={2}(1 way), h={0}(1 way) t={0,1}−{0}={1}(1 way) u={1,3,5,7,9}−{0,1,9}={3,5,7}(3 ways Total ways(numbers) upto 2019 (except 2019) 1×1×1×3=3(to be subtracted) [ These numbers are 2013,2015 & 2017 ] Total of required numbers from 2019 to 9102 =28+672+840+280−3=1817](https://www.tinkutara.com/question/Q51374.png)