Question

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

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (C)

$5$

Six digit number formed by $(1,2,3,4,5,6,7)$ are arranged in descending order.

$7⟶7\_\_\_\_\_{}_{}^6{P}_5=720$

$6⟶6\_\_\_\_\_{}_{}^6{P}_5=720$

$5⟶5\_\_\_\_\_{}_{}^6{P}_5=720$

$4⟶4\_\_\_\_\_{}_{}^6{P}_5=720$

$3⟶37\_\_\_\_{}_{}^5{P}_4=120$

$7⟶367542{}_{}$

$367542$