Question

Find the sum of all numbers greater than $10000$ formed by using digits $1,3,5,7,9$, no digit being repeated in any number.

Answer 1

Let us consider for understanding $3$ numbers
$1$ $2$ $3$
$2$ $1$ $3$
$3$ $1$ $2$
$1$ $3$ $2$
$2$ $3$ $1$
$3$ $2$ $1$
So, from here, we can understand each of the digit come to $100th,$ $10th,$ and unit's place for $(n-1)!$ times.
$\therefore$ sum of numbers formed = (sum of digits)$\times$$({10}^{n-1}+{10}^{n-2}+....1)\times (n-1)!$
So for $1,3,5,7,9,$ we get:-
Sum $=(1+3+5+7+9)\times ({10}^4+{10}^3+{10}^2+10+1)\times 4!$
$=25\times 11111\times 24$
$=6666600$