JEE Advanced Mathematics question
Consider all possible permutations of letters of the word ENDEANOEL. Column I: (A) The number of permutations containing the word ENDEA is (B) The number of permutations in which the letter E occurs in the first and the last positions is (C) The number of permutations in which none of the letters D, L, N occurs in the last five positions (D) The number of permutations in which the letters A, E, O occur only in odd positions is Column II: (p) (q) (r) (s)
Solution
ENDEANOEL has 9 letters: E×3, N×2, D, A, O, L. (All counts confirmed by brute-force enumeration of the 30240 distinct arrangements.)
- **(A)** Treat "ENDEA" as one block; the remaining letters are N, O, E, L (all distinct). Arrange 5 distinct objects: . A–p. - **(B)** Fix E at both ends; the middle 7 letters
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