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 :

• A. $77$
• B. $42$
• C. $35$
• D. $82$

Answer 1

The correct option is A $77$

CASE -I : $1,1,1,1,1,2,3$
Number of ways $=\frac{7!}{5!}=42$
CASE -II : $1,1,1,1,2,2,2$
Number of ways $=\frac{7!}{4!\times 3!}=35$
Total number of ways $=42+35=77$