Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in…
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.
(A) r, (B) q, (C) s, (D) p
(A) p, (B) s, (C) q, (D) q
(A) p, (B) r, (C) s, (D) q
(A) r, (B) s, (C) r, (D) p
Solution
(A) If ENDEA is fixed word, then assume this as a single letter.
Total number of letters $=5$ and total number of arrangements $=5$ ! .
(B) If $E$ is at first and last places, then total number of permutations
$
\frac{7 !}{2 !}=21 \times 5 !
$
(C) If $\mathrm{D}, \mathrm{L}, \mathrm{N}$ are not in last five positions
$
\leftarrow \mathrm{D}, \mathrm{L}, \mathrm{N}, \mathrm{N} \rightarrow \leftarrow \text { E, E, E, A, O } \rightarrow
$
Total number of permutations $=\frac{4 !}{2 !} \times \frac{5 !}{3 !}=2 \times 5$ ! .
(D) Total number of odd positions $=5$
Permutations of AEEEO are $\frac{5 !}{3 !}$
Total number of even positions $=4$
Number of permutations of $\mathrm{N}, \mathrm{N}, \mathrm{D}, \mathrm{L}=\frac{4 !}{2 !}$
Hence, total number of permutations $=\frac{5 !}{3 !} \times \frac{4 !}{2 !}=2 \times 5 !$
