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

Suggest corrections