Verified Solution • 2025–26 Session moderate

QJEEM21Ma065d: JEE Main 2021 Mathematics - Class 11 JEEM21Ma065d Solution: The number of seven digit integers with sum of the digits equal …

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 :

Multiple Choice Options

  • A 35
  • B 42
  • C 82
  • D 77

Step-by-Step Verified Solution

(I) First possibility is 1, 1, 1, 1, 1, 2, 3

required number = 7!5!{{7!} \over {5!}} = 7 ×\times 6 = 42

(II) Second possibility is 1, 1, 1, 1, 2, 2, 2

required number = 7!4!3!=7×6×56=35{{7!} \over {4!3!}} = {{7 \times 6 \times 5} \over 6} = 35

Total = 42 + 35 = 77

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