Question

# The sum of all possible numbers greater than 10,000 formed by using {1,3,5,7,9} is

- 6666600
- 932460
- 6660000
- 1968

Hint:

### First of all find the total number of numbers satisfying the given conditions. Now fix 4 out of 5 digits each time and divide total numbers into 5 categories and then consider the place value of each digit of 5 categories to find the total sum of numbers.

## The correct answer is: 6666600

### Detailed Solution

In this, we have to find the sum of all numbers greater than 10000 formed by using digits 1, 3, 5, 7, 9, no digit being repeated in any number. We know that any number greater than 10000 would be of 5 digits or more than 5 digits. Also, since we have only 1, 3, 5, 7, 9, and repetition is not allowed, we can make only 5 digit numbers and any number formed by these five digits would be greater than 10000.

Any of the five digits can occupy ten thousand places. Since repetition is not allowed any of the remaining 4 digits can occupy a thousand’s place. Similarly, any of the remaining 3 digits can occupy a hundred’s place.

Now, ten’s and unit’s place can be occupied by any of the remaining two digits and last remaining digit respectively.

Therefore, we get the sum of total numbers greater than 10000 formed by using digits 1, 3, 5, 7, 9 without repetition is 6666600.

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