Question
The sum of all the numbers formed by taking all the digits from 3,4,5,6,7 is:
- 6666600
- 566666600
- 6656600
- 6665600
Hint:
To find the sum of all the numbers formed with 3,4,5,6,7, it is necessary to know in how many numbers each of 3,4,5,6,7 will be in the unit place. Then we can find the sum of all the numbers in the unit place similarly we will find the sum of all the numbers in tens, hundreds, thousands and ten thousands place. At last, we will find the required sum.
The correct answer is: 6666600
The number of numbers having 3 in the unit place= 4! =24
The number of numbers having 4 in the unit place= 4! =24
The number of numbers having 5 in the unit place= 4! =24
The number of numbers having 6 in the unit place= 4! =24
The number of numbers having 7 in the unit place= 4! =24
So the sum of the digits in the unit place of all the numbers=
=24(3+4+5+6+7)
=24
25=600
Similarly the sum of the digits of all the numbers in each of the other places=600
The required sum =
=600(10000+1000+100+10+1)
=600(11111)
=6666600
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