Question

All the six distinct digit numbers made by digits taken from the set {1, 2, 3, 4, 5, 6, 7} are arranged in descending order. The digit at hundreds place in ${3001}^{th}$ number is

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (C)

5

Consider the $6$ digit numbers where the left most digit is $7$. The remaining $5$ places can be filled in $6!=720$. Hence the $721st$ number in the order will have $6$ as the left most digit and there will be $720$ such number starting with $6$.
Similarly there will be $1440$ numbers where the left most digit is $5$ or $4$,Hence there are $720+720+720+720=2880$ numbers whose left most digit is $4$ or bigger and the $2881st$ will have $3$ as the leftmost digit.
Now there will be $5!=120$ number which "37" as the two leftmost digits.
The total numbers in the order are $2880+120=3000$
Hence the next number will be $367542$.