HOW TO FIND SUM OF ALL 4 DIGIT NUMBERS FORMED USING THE DIGITS

Here we are going to see how to find sum of all 4 digit numbers formed using the given digits 1, 2, 3, 4 and 5.

Let us look at some examples to understand the above concept.

Example 1 :

Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed ?

Solution :

Since we form a 4 digit number, let us create 4 places.

____    ____    ____    ____

Total number can be formed with the unit digit 1

 2 ⋅ 3 ⋅ 4 ⋅ 1  =  24

Total number can be formed starting with the digit 2

 2 ⋅ 3 ⋅ 4 ⋅ 1  =  24

Total number can be formed starting with the digit 3

 2 ⋅ 3 ⋅ 4 ⋅ 1  =  24

Total number can be formed starting with the digit 4

 2 ⋅ 3 ⋅ 4 ⋅ 1  =  24

Total number can be formed starting with the digit 5

 2 ⋅ 3 ⋅ 4 ⋅ 1  =  24

So, totally we may form 5(24)  =  120 numbers using the given digits.

From the above steps, we may understand that we may see the number 1 in 24 times in the unit place.

Sum of digits in the unit place 

  =  (1 ⋅ 24) + (2 ⋅ 24) + (3 ⋅ 24) + (4 ⋅ 24) + (5 ⋅ 24)

  =   360

Sum of digits in the ten's place 

  =  (1 ⋅ 24) + (2 ⋅ 24) + (3 ⋅ 24) + (4 ⋅ 24) + (5 ⋅ 24)

  =   360 ⋅ 10  =  3600

Sum of digits in the hundred's place 

  =  (1 ⋅ 24) + (2 ⋅ 24) + (3 ⋅ 24) + (4 ⋅ 24) + (5 ⋅ 24)

  =   360 ⋅ 100  =  36000

Sum of digits in the hundred's place 

  =  (1 ⋅ 24) + (2 ⋅ 24) + (3 ⋅ 24) + (4 ⋅ 24) + (5 ⋅ 24)

  =   360 ⋅ 1000  =  360000

Hence the sum of all 4 digit numbers formed with the given digits   

=   360000 + 36000 + 3600 + 360

=  399960

Example 2 :

Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?

Solution :

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