Question

The sum of all numbers grater than $10000$ formed by using the digits $1,3,5,7,9$ no digit being repeated in any number is

• A. $4666600$`
• B. $5666600$
• C. $6666600$
• D. None of these

Answer 1

Answer: (C)

$6666600$

All the numbers are of $5$ digits.

The number of numbers having $1$ in unit's place $=$ number of arrangement of the remaining $4$ digits $={{}^{4}P}_4=24$

Similarly, for other digits also each digit occurs $24$ times in units place.

So the sum of digits in unit's place for all numbers$=24\times 1+24\times 3+24\times 5+24\times 7+24\times 9=600$

Similarly, the number of digits in each of the other places$=600$

Thus the required sum$=600\times 10000+600\times 1000+600\times 100+600\times 10+600\times 1=6666600$