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

We have to form 7digit numbers, using the digits 1, 2 and 3 only, such that the sum of the digits in a number = 10 .
This can be done by taking 2,2,2,1,1,1,1,or by taking 2,3,1,1,1,1,1.
$\therefore$ Number of ways $=\frac{7!}{3!4!}+\frac{7!}{5!}=77.$