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JEE Main 20169 AprilOnline
Exam
JEE Main
Year
2016
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2016 · 9 April · Online · Mathematics · Permutation and Combination

If the four letter words (need not be meaningful) are to be formed...

If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is RR and the fourth letter is EE, then the total number of all such words is :

Options

  1. A110110
  2. B5959
  3. C\dfrac{11 !}{{\left(2 !\right)}^{3}}
  4. D5656

Correct answer

B. 5959

Step-by-step solution

M,EEE,D,I,T,RR,AA,NNM, EEE, D, I, T, RR, AA, NN

\mathop{R}_{_}\mathop{}_{_}\mathop{}_{_}\mathop{E}_{_}

Two empty places can filled with identical letters \left[EE, AA, NN\right] ⇒ 3ways<br/><br/>Twoemptyplaces,canbefilledwithdistinctletters[M,E,D,I,T,R,A,N]⇒8P2ways<br /><br />Two empty places, can be filled with distinct letters \left[M, E, D, I, T, R, A, N\right] ⇒ {}^{8}{P}_{2}

∴∴ Number of words 3+8P2=593 + {}^{8}{P}_{2} = 59
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