The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1 , 2…

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. 77
  2. 82
  3. 42
  4. 35

Solution

I First possiblity is 1,1,1,1,1,2,3

required number =7!5!=7×6=42

II Second possiblity is 1,1,1,1,2,2,2

required number =7!4!3!=7×6×56=35

Total =42+35=77

Asked in: JEE Main 2021 (26 Feb Shift 1)

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