How to Calculate the Sum of 5-Digit Numbers Using Specific Digits?

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The discussion focuses on calculating the total sum of 5-digit numbers formed using the digits 0, 1, 2, 3, 4, 5, and 6, with specific cases for repetition. Users explore two scenarios: forming numbers without digit repetition and with digit repetition. The main challenge identified is calculating the sum for cases where digits are repeated, particularly when two digits are the same or when two pairs of digits are the same. Participants seek clarification on the mathematical approach to derive these sums accurately.

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The Total Sum of $5$ Digit no. which can be formed with the Digit $0,0,1,1,2,2,3,3,4,4,4,5,6$

[a] without Repetition of Digit.

with Repetition of Digit
 
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jacks said:
The Total Sum of $5$ Digit no. which can be formed with the Digit $0,0,1,1,2,2,3,3,4,4,4,5,6$

[a] without Repetition of Digit.

with Repetition of Digit


Hi jacks, :)

I don't understand why you have repeated the digits. Is your problem,

"Find the Total sum of $5$ digit numbers which can be formed with the digits $0,1,2,3,4,5,6$" ?
 
Oh Sorry Sudhakara The question is The Sum of $5$ Digit no. using the Digi $1,2,2,3,4,5,5$

My Try: I have formed Three cases

(I) When all Digits are Distinct

(II) When Two are same like $22134,22135,12355,12455$

(II) When two are of one kind and other two are of other kind. like $2255$

But I Did not Understand How can I calculate sum in (II) and (III) cases.

please help me . Thanks
 

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