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 positions, is	(r) \(7 \times 5!\)
(D) The number of permutations in which the letters A, E, O occur only in odd positions, is	(s) \(21 \times 5!\)

(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 \(=\frac{5 !}{3 !} \times \frac{4 !}{2 !}=2 \times 5 !\).