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 × 4 matrix given

Question

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 × 4 matrix given in the ORS. [2008]

	Column I		Column II
(A)	The number of permutations containing the word ENDEA is	(p)	5!
(B)	The number of permutations in which the letter E occurs in the first and the last positions is	(q)	2 × 5!
(C)	The number of permutations in which none of the letters D, L, N occurs in the last five positions is	(r)	7 × 5!
(D)	The number of permutations in which the letters A, E, O occur only in odd positions is	(s)	21 × 5!

Smart Achievers · Accepted Answer

(4)

(A) For the permutations containing the word ENDEA we consider 'ENDEA' as single letter. Then we have total ENDEA, N, O, E, L i.e. 5 letters which can be arranged in 5! ways.

$∴$ $(A) \to (p)$

(B) If E occupies the first and last position, the middle 7 positions can be filled by N, D, E, A, N, O, L in
$\frac{7!}{2!} = 7 \times 6 \times 5 \times 4 \times 3 = 21 \times 120 = 21 \times 5!$ ways.

$∴$ $(B) \to (s)$

(C) If none of the letters D, L, N occur in the last five positions then we should arrange D, L, N, N at first four positions and rest five i.e. E, E, E, A, O at last five positions. This can be done in
$\frac{4!}{2!} \times \frac{5!}{3!} = 4 \times 3 \times \frac{5!}{3 \times 2} = 2 \times 5!$ ways.

$∴$ $(C) \to (q)$

(D) As per question A, E, E, E, O can be arranged at 1st, 3rd, 5th, 7th and 9th positions and rest D, L, N, N at remaining 4 positions. This can be done in
$\frac{5!}{3!} \times \frac{4!}{2!} ways = 2 \times 5!$ ways.

$∴$ $(D) \to (q)$

Solution

1 $(A) \to (q); (B) \to (s); (C) \to (q); (D) \to (p)$

2 $(A) \to (q); (B) \to (q); (C) \to (s); (D) \to (p)$

3 $(A) \to (s); (B) \to (q); (C) \to (q); (D) \to (p)$

4 $(A) \to (p); (B) \to (s); (C) \to (q); (D) \to (q)$

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Solution

1 (A)→(q); (B)→(s); (C)→(q); (D)→(p)

2 (A)→(q); (B)→(q); (C)→(s); (D)→(p)

3 (A)→(s); (B)→(q); (C)→(q); (D)→(p)

4 (A)→(p); (B)→(s); (C)→(q); (D)→(q)

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1 $(A) \to (q); (B) \to (s); (C) \to (q); (D) \to (p)$

2 $(A) \to (q); (B) \to (q); (C) \to (s); (D) \to (p)$

3 $(A) \to (s); (B) \to (q); (C) \to (q); (D) \to (p)$

4 $(A) \to (p); (B) \to (s); (C) \to (q); (D) \to (q)$