Question

All the 7 digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once and not divisible arranged in the increasing oder then-

• A. ${1800}^{\text{th}}$ number in the list 3142567
• B. ${1897}^{\text{th}}$ number in the list is 4231567
• C. ${1994}^{\text{th}}$ number in the list is 4321567
• D. ${2004}^{\text{th}}$ number in the list is 4316527

Answer 1

The correct option is D ${2004}^{\text{th}}$ number in the list is 4316527

Numbers which are not divisible by 5

Unit's place cannot hold 5

that is $6.6!=4320$

Number of numbers starting with

$1:5\times 5\times 4\times 3\times 2\times 1=600$

$2:5\times 5\times 4\times 3\times 2\times 1=600$

$3:5\times 5\times 4\times 3\times 2\times 1=600$

$4:5\times 5\times 4\times 3\times 2\times 1=600$

Adding all these we get $600+600+600+600=2400$

$1800<2004<2400$

$20003$rd number in the list is $4316257$

$2004$ th number in the list is $4316527$