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AIEEE 2002

JEE Main 2002 Mathematics question on Permutations and Combinations

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is
  1. A.
    40
  2. B.
    60
  3. C.
    80
  4. D.
    100
Show answer and solution

Correct option: A

Solution

Total arrangements of BANANA (3 A's, 2 N's, 1 B) = 6!/(3!·2!) = 60.

Arrangements where the 2 N's ARE adjacent: treat NN as one unit, giving 5 letters (NN, B, A, A, A) → 5!/3! = 20.

Non-adjacent arrangements = 60 - 20 = 40.

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