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JEE Main 202126 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
26 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2021 · 26 February · Morning Shift · Mathematics · Permutation and Combination

The number of seven digit integers with sum of the digits equal to...

The number of seven digit integers with sum of the digits equal to 1010 and formed by using the digits 1,21, 2 and 33 only is:

Options

  1. A7777
  2. B8282
  3. C4242
  4. D3535

Correct answer

A. 7777

Step-by-step solution

(I)\left(I\right) First possiblity is 1,1,1,1,1,2,31, 1, 1, 1, 1, 2, 3

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

(II)\left(II\right) Second possiblity is 1,1,1,1,2,2,21, 1, 1, 1, 2, 2, 2

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

Total =42+35=77= 42 + 35 = 77

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