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. 55
• B. 66
• C. 77
• D. 88

Answer 1

Answer: (C)

77

Answer 2

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