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

Answer: (A)

Case-1 :

$1,1,1,1,1,2,3$
Number of ways $=\frac{7!}{5!}=42$ [Since, $1$ repeat five times]
Case- 2 :

$1,1,1,1,2,2,2$
Number of ways $=\frac{7!}{4!\times 3!}=35$ [Since, $4$ repeat four times and $2$ repeat three times ]

Total number of ways $=42+35=77$