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

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	$2\times 5!$
C	The number of permutations in which none of the letters $D,L,N$ occurs in the last five	r	$7\times 5!$ positions is
D	The number of permutations in which the letters $A,E,O$ occur only in odd positions is	s	$21\times 5!$

• A. $(A)\to (P);(B)\to (S);(C)\to (Q);(D)\to (Q)$
• B. $(A)\to (P);(B)\to (S);(C)\to (Q);(D)\to (P)$
• C. $(A)\to (P);(B)\to (Q);(C)\to (Q);(D)\to (S)$
• D. $(A)\to (Q);(B)\to (S);(C)\to (R);(D)\to (P)$

Answer 1

Answer: (A)

(A) ENDEA, $N,O,E,L$ are five different letter, then permutation $=5!$
(B) If $E$ is in the first and last position then
$\frac{(9-2)!}{2!}=7\times 3\times 5!=21\times 5!$
(C) for first four letters $=\frac{4!}{2!}$
for last five letters $=5!/3!$
Hence $\frac{4!}{2!}\times \frac{5!}{3!}=2\times 5!$
(D) For $A,E$ and $O5!/3!$ and for others $4!/2!$
hence $\frac{5!}{3!}\times \frac{4!}{2!}=2\times 5!$