The number of seven digit integers

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

  1. (1) 77

  2. (2) 42

  3. (3) 35

  4. (4) 82


Correct Option: 1

Solution:

CASE-I: $1,1,1,1,1,2,3$

$\mathrm{WAYS}=\frac{7 !}{5 !}=42$

CASE-II: $1,1,1,1,2,2,2$

WAYS $=\frac{7 !}{4 ! \cdot 3 !}=35$

TOTAL WAYS $=42+35=77$

Leave a comment