Question

Five digit numbers can be formed of $1,3,5,7,9$. What will be the sum of all the numbers.

• A. $2222200$
• B. $4444400$
• C. $6666600$
• D. none of these

Answer 1

Answer: (C)

$6666600$

Given digits : $1,3,5,7,9$

Number of digit $=n=5$

Sum of digits $=1+3+5+7+9=25$

Sum of all five digit numbers

$=$(Sum of $n$ digits )$(n-1)!$(${10}^{n-1}+{10}^{n-2}+.......{10}^1+{10}^0$)

$=25(4!)({10}^4+{10}^3+{10}^2+10+1)$

$=25\left(24\right)\left(1111\right)$

$=6666600$