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)

$6666600$

Answer 2

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 $= 25\left(10^{4} + 10^{3} +10^{2} + 10 + 1\right)\times 4!$ $= 600 \times\frac{ 10^{5} -1}{10 -1 }$ $= 600 \times 11111$ $= 6666600$.