Question

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

• A. $55$
• B. $66$
• C. $77$
• D. $88$

Answer 1

Answer: (C)

$77$

There are two possible cases
Case 1: Five 1's, one 2's, one 3's
Number of numbers $=\frac{7!}{5!}=42$
Case 2: Four 1's, three 2's
Number of numbers $=\frac{7!}{4!3!}=35$
Total number of numbers $=42+35=77$