The number of seven digit

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. 42

  2. 82

  3. 77

  4. 35


Correct Option: , 3

Solution:

(I) First possiblity is $1,1,1,1,1,2,3$

required number $=\frac{7 !}{5 !}=7 \times 6=42$.

(II) Second possiblity is $1,1,1,1,2,2,2$

required number $=\frac{7 !}{4 ! 3 !}=\frac{7 \times 6 \times 5}{6}=35$

Total $=42+35=77$

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