Permutations and Combinations Part 1

To form a seven digit number with sum of digits 10 , all the digits can't be 1,2 or 3.
Hence, seven digit number must have the following cases,
Case 1. Using 1, 1, 1, 1, 1,2,3
Possible seven digit numbers will be =‌

7!

5!

=7×6=42
Case 2. Using 2, 2, 2, 1, 1, 1, 1
Possible numbers will be =‌

7!

3!4!

=‌

7×6×5

3×2

=35
No more cases will be formed.
Hence, total number of seven digit numbers possible =42+35=77