Question

The sum of all numbers greater than $1000$ formed by using digits $1$, $3$, $5$, $7$ no digit being repeated in any number is

• A. $72$, $215$
• B. $83$, $911$
• C. $106$, $656$
• D. $114$, $712$

Answer 1

Answer: (C)

Reqd. sum $=3!\left[1+3+5+7\right]\left[1+10+100+1000\right]$
$=96\left(1111\right)=106,656$
[$\because$ each digit occurs $3!$ times in unit place tens place, hundreds place and thousands place.]