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.
Related Questions to study
Number of different permutations of the word 'BANANA' is
In this question, one might think that the total number of permutations for the word BANANA is 6!
This is wrong because in the word BANANA we have the letter A repeated thrice and the letter N repeated twice.
Number of different permutations of the word 'BANANA' is
In this question, one might think that the total number of permutations for the word BANANA is 6!
This is wrong because in the word BANANA we have the letter A repeated thrice and the letter N repeated twice.
The number of one - one functions that can be defined from 
into 
is
The number of one - one functions that can be defined from into is
Four dice are rolled then the number of possible out comes is
Four dice are rolled then the number of possible out comes is
The number of ways in which 5 different coloured flowers be strung in the form of a garland is :
The number of ways in which 5 different coloured flowers be strung in the form of a garland is :
Number of ways to rearrange the letters of the word CHEESE is
Number of ways to rearrange the letters of the word CHEESE is
The number of ways in which 17 billiard balls be arranged in a row if 7 of them are black, 6 are red, 4 are white is
We cannot arrange the billiards balls as follows:
There are 17 balls, so the total number of arrangements = 17!
This is incorrect because this method is applicable only when the balls are distinct, not identical. But, in our case, all the balls of the same color are identical.
The number of ways in which 17 billiard balls be arranged in a row if 7 of them are black, 6 are red, 4 are white is
We cannot arrange the billiards balls as follows:
There are 17 balls, so the total number of arrangements = 17!
This is incorrect because this method is applicable only when the balls are distinct, not identical. But, in our case, all the balls of the same color are identical.
Number of permutations that can be made using all the letters of the word MATRIX is
Number of permutations that can be made using all the letters of the word MATRIX is
The number of different signals that can be made by 5 flags from 8 flags of different colours is :
Each of the different arrangements which can be made by taking some or all of a number of things at a time is called permutation. 
Thus we can say that the permutation concerns both the selection and the arrangement of the selected things in all possible ways.
The number of different signals that can be made by 5 flags from 8 flags of different colours is :
Each of the different arrangements which can be made by taking some or all of a number of things at a time is called permutation.
Thus we can say that the permutation concerns both the selection and the arrangement of the selected things in all possible ways.
then A-B=
, then 
then K=
when divided by 
and 
are 7,3 then the remainder of 
is
then 
are
are
