MHB 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 from specific digits, including cases with and without repetition. Participants express confusion about handling repeated digits and how to calculate sums in different scenarios. The main cases identified include distinct digits, two identical digits, and two pairs of identical digits. The need for clarification on the calculation methods for these cases is emphasized. Overall, the conversation seeks guidance on accurately summing these combinations.
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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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