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Question

If 6 digit number is made using all the digits 1,2,4,5,7,8, then the position of number ′′541782′′ when all numbers formed are arranged in descending order is 


Solution

Available digits: 1,2,4,5,7,8
Since the numbers had to be arranged in decreasing order.
Total number starting from 8 (8 _ _ _ _ _) will be 5!
Total number starting from 7  (7 _ _ _ _ _)  will be 5!
Now the total numbers starting from 58  (58 _ _ _ _)  will be 4!
Total numbers starting from 57   (57 _ _ _ _) will be 4!
Now the total numbers starting from 548   (548 _ _ _) will be 3!
The total numbers starting from 547   (547 _ _ _) will be 3!
The total numbers starting from 542   (542 _ _ _) will be 3!
Now the total numbers starting from 5418   (5418 _ _) will be 2!
Now the next number will be ′′541782′′
Total number before ′′541782′′ are 5!+5!+4!+4!+3!+3!+3!+2!=308
The required position of ′′541782′′  will be 309
 

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