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JEE Main 20188 April
Exam
JEE Main
Year
2018
Date
8 April
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2018 · 8 April · Mathematics · Permutation and Combination

From 6 different novels and 3 different dictionaries, 4 novels and...

From 66 different novels and 33 different dictionaries, 44 novels and 11 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:

Options

  1. AAt least 750750 but less than 10001000
  2. BAt least 10001000
  3. CLess than 500500
  4. DAt least 500500 but less than 750750

Correct answer

B. At least 10001000

Step-by-step solution

N1,N2,D,N3,N4{N}_{1}, {N}_{2}, D, {N}_{3}, {N}_{4}

N→N \to Novels

D→D \to Dictionary

DD can be chosen in 33 ways

N1→6{N}_{1} \to 6

N2→5{N}_{2} \to 5

N3→4{N}_{3} \to 4

N4→3{N}_{4} \to 3

Total ways =3×6×5×4×3=1080= 3 \times 6 \times 5 \times 4 \times 3 = 1080
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