Question

The sum of all the numbers which are greater than $10000$ formed by the digits $1,3,5,7,9$ using each digit only once is:

• A. $666000$
• B. $666600$
• C. $6666600$
• D. $66666600$

Answer 1

The correct option is C $6666600$

Total numbers formed $=5!=120$
Since, we have 5 digits 1,3,5,7,9 . Let $x$ be the digit at 10,000's place , so the remaining digits can be arranged in $4!=24$ ways.
i.e $x$ occurs at 10,000's place in 24 numbers.
Sum at 10,000's place $=24\times 10,000\times (1+3+5+7+9)=6000000$
Sum at 1000's place $=24\times 1000\times (1+3+5+7+9)=600000$
Sum at 100's place $=24\times 100\times (1+3+5+7+9)=60000$
Sum at 10's place $=24\times 10\times (1+3+5+7+9)=6000$
Sum at ones place $=24\times 1\times (1+3+5+7+9)=600$
Required sum $=6666600$