Question

Find the sum of all the 4 digit numbers that can be formed with the digits 3, 4, 5 and 6

Answer 1

the answer to question is attached in the pic

Answer 2

When the total numbers will be =N

Then the formula will be :-

=(Sum of all numbers)×( total number of all numbers - 1)×( 1.... N times)

=(N)×(N-1)!×(1…N times)

Here if we keep 6as unit digit,other three numbers will give us 6 possible combinations.So 6 will come six times at the unit digit, similarly we have to think for other digits.

∴ 3 ,4,5,6 every number will come six times. So There sum would be (unit digit sum) :-

(3+4+5+6) ×6 or (3+4+5+6)×3.

=18×6=108

• Here what have we done for unit digit,
• we apply same logic for other digits decimal,
• hundredths, thousands.The digit sum should be 108.
• To get sum of all numbers will consider their weights .

Therefore now we get,

⇒(108×1000)+(108×100)+(108×10)+108

⇒108(1000+100+10+1)

⇒108×1111

⇒119,988

Let us formulate this :-

(3+4+5+6) ×3×1111

Ans :- The sum of all the 4 digit numbers that can be formed with the digits 3, 4, 5 and 6  will be 119,988.

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