Question

The sum of all the five digit numbers that can be formed by taking digits $2,3,4,4,5$ only once is

• A. 2399976
• B. 2339976
• C. 2333976
• D. 2399376

Answer 1

The correct option is A 2399976

First find the number of $5$ digit numbers which has $5$ at unit's place.
When $5$ is at unit's place, the remaining $4$ places can be filled by $2,3,4,4$ in $\frac{4!}{2!}=12$
Similarly when $4,3$ and $2$ are at unit's place we get $24,12,12$ five digit numbers respectively.
So when we add all such numbers obtained the total sum of units' place digits will be $12(5+3+2)+24\times 4=216$.
Same pattern will follow for other places as well.
Hence, the total sum$=({10}^4+{10}^3+{10}^2+10+1)216=2399976$