JEE Advanced 2008 Paper 2Question 1
Consider all possible permutations of the letters of the word ENDEANOEL.
Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $4\times4$ matrix given in the ORS.
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 is
(D) The number of permutations in which the letters A, E, O occur only in odd positions is
Column II:
(p) $5!$
(q) $2\times5!$
(r) $7\times5!$
(s) $21\times5!$
Permutation and Combination
AnswerA-p, B-s, C-q, D-q
Solution
(A) ENDEA as a block with E,N,O,L gives $5!$. (B) E at both ends: $7!/2!=21\cdot5!$. (C) D,L,N,N fill first four places in $4!/2!=12$ ways, E,E,E,A,O the rest in $20$: $240=2\cdot5!$. (D) A,E,O in the 5 odd places: $20$ ways, D,L,N,N in even places: $12$; $240=2\cdot5!$.