The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits

Question

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

Professor PC Thomas Classes · Answer

The digits forming the number can be 1) $1,1,1,1,1,2,3$ or 2 ) $1,1,1,1,2,2,2$ With the digits in (1) $\frac{7!}{5!}=42$ numbers can be formed with the digits in (2) $\frac{7!}{4!3!}=35$ numbers can be formed . Total 77 numbers