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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.
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Verified Answer
The correct answer is:
(A) p, (B) s, (C) q, (D) q
(A) p, (B) s, (C) q, (D) q
(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 $=\frac{5 !}{3 !} \times \frac{4 !}{2 !}=2 \times 5 !$.
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 $=\frac{5 !}{3 !} \times \frac{4 !}{2 !}=2 \times 5 !$.
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