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

The correct option is C 77

The digits are 1, 1, 1, 1, 1, 2, 3
or 1, 1, 1, 1, 2, 2, 2
Hence number of seven digits numbers formed
$=\frac{7!}{5!}+\frac{7!}{4!3!}=77$.