The number of seven digit positive integers formed using the digits 1, 2,3 and 4 only and sum of the digits equal to 12 is________.
Text Solution
Verified by Experts413
(413)
The given numbers are 1, 2,3,4 and sum of digits should be 12.
Case 1: 4 3 1 1 1 1 1, Here me sum of me digits is 12.
The number of ways arranging them is = 
= 42.
The number of ways arranging them is = 
= 105
Case 3: 3222111.
The number of ways arranging them is = 
= 140
Case 4: 3 3 2 1 1 1 1
The number of ways arranging them is = 
= 105
Case 5: 2 2 2 2 2 1 1
The number of ways arranging them is = 
=21
The total number of ways are = 42 + 105 + 140 + 105 + 21
= 413
Therefore, the required answer is 413.
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