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JEE Main 20206 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2020 · 6 September · Morning Shift · Mathematics · Permutation and Combination

Two families with three members each and one family with four...

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?

Options

  1. A2!3!4!2 ! 3 ! 4 !
  2. B(3!)3⋅(4!)( 3 ! {)}^{3} \cdot ( 4 ! )
  3. C(3!)2.(4!)( 3 ! ) 2 . \left(4 !\right)
  4. D\text{3!}{\left(4 !\right)}^{3}

Correct answer

B. (3!)3⋅(4!)( 3 ! {)}^{3} \cdot ( 4 ! )

Step-by-step solution

We will use the concept 'objects are together'

3!⏟Total 3 families×(3!)2⏟families with all 3 members together×4!⏟family with all 4 together\mathop{\mathop{3 !}_{⏟}}_{\text{Total 3 families}} \times \mathop{\mathop{{\left(3 !\right)}^{2}}_{⏟}}_{\text{families with all 3 members together}} \times \mathop{\mathop{4 !}_{⏟}}_{\text{family with all 4 together}}

=(3!)3×4!= ( 3 ! {)}^{3} \times 4 !

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