Question

The sum of $5$ digit numbers in which only odd digits occur without any repetition is

• A. $277775$
• B. $555550$
• C. $1111100$
• D. $6666600$

Answer 1

Answer: (D)

The digits that make the numbers are $1,3,5,7$ and $9$.
The number of numbers with one of these in the first place $=4!$.
$\therefore$ The required sum of all the numbers
$=25\left(10^4+10^3+10^2+10+1\right)\times 4!$
$=600\times \frac{10^5-1}{10-1}$
$=600\times 11111$
$=6666600$.