Available digits: 1,2,4,5,7,8
Since the numbers had to be arranged in increasing order.
Total number starting from 1 (1 _ _ _ _ _) will be 5!
Total number starting from 2 (2 _ _ _ _ _) will be 5!
Total number starting from 4 (4 _ _ _ _ _) will be 5!
Now the total numbers starting from 51 (51 _ _ _ _) will be 4!
Total numbers starting from 52 (52 _ _ _ _) will be 4!
Now the total numbers starting from 5412 (5412 _ _) will be 2!
Now the total numbers starting from 54172 (54172 _) will be 1 only
Now the next number will be ′′541782′′
Total number before ′′541782′′ are 5!+5!+5!+4!+4!+2!+1=411
∴ The position of ′′541782′′ in increasing order will be 412