The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1 , 2 and 3 only is:

Step-by-step solution

I First possiblity is 1 , 1 , 1 , 1 , 1 , 2 , 3 required number = 7 ! 5 ! = 7 × 6 = 42 II Second possiblity is 1 , 1 , 1 , 1 , 2 , 2 , 2 required number = 7 ! 4 ! 3 ! = 7 × 6 × 5 6 = 35 Total = 42 + 35 = 77