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 _ _ _ _ _ _ _ .

Step-by-step solution

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 the sum of the digits is 12 . The number of ways arranging them is = 7 ! 5 ! = 42 . Case 2 :   4   2   2   1   1   1   1 . The number of ways arranging them is = 7 ! 2 ! 4 ! = 105 Case 3 :   3   2   2   2   1   1   1 . The number of ways arranging them is = 7 ! 3 ! 3 ! = 140 Case 4 :   3   3