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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2017 · Mathematics · Permutation and Combination

A tea party is arranged for 16 people along two sides of a long...

A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is

Options

  1. A24×8!×8!24 \times 8!\times 8!
  2. B(81)3(81)^3
  3. C210×8!×8210 \times 8!\times 8 !
  4. D16!16!

Correct answer

C. 210×8!×8210 \times 8!\times 8 !

Step-by-step solution

Number of ways =8!8!4!6!×10!=(8!)2×10!4!6!=(8!)2×10×9×8×74!=(8!)2×10×9×8×74×3×2×1=(210)×(8!)2=\frac{8!8!}{4!6!} \times 10!=(8!)^2 \times \frac{10!}{4!6!}=(8!)^2 \times \frac{10 \times 9 \times 8 \times 7}{4!}=(8!)^2 \times \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1}=(210) \times(8!)^2
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