Match the counts for n distinct questions or objects. Column I: (A) Answer one or more of n questions (B) Answer one or more questions, each with an alternative answer (C) Circular permutations of n o

Question

Match the counts for n distinct questions or objects. Column I: (A) Answer one or more of n questions (B) Answer one or more questions, each with an alternative answer (C) Circular permutations of n objects, taken r at a time (D) Same as C but identify clockwise with anticlockwise Column II: (p) n ​ P r ​ / ( 2 r ) ( q ) 2 n ( r ) n ​ P r ​ / r ( s ) 3 n − 1 ( t ) 2 n − 1 Column I Column II (A) Answer one or more of n questions (p) n ​ P r ​ / ( 2 r ) (B) Answer one or more questions, each with an alternative answer (q) 2 n (C) Circular permutations of n objects, taken r at a time (r) n ​ P r ​ / r (D) Same as C but identify clockwise with anticlockwise (s) 3 n − 1 (t) 2 n − 1

TestHub · Accepted Answer

Each question has two choices in A (answer or omit), three in B (first alternative, second, omit); remove the all-omitted case. A circular word has r equivalent rotations; for r ≥ 3 , reflection halves the orientation-distinguished count. For r = 1 , 2 the printed D expression requires special treatment.

Column I	Column II
(A) Answer one or more of $n$ questions	(p) $_{n} P_{r} / (2 r)$
(B) Answer one or more questions, each with an alternative answer	(q) $2^{n}$
(C) Circular permutations of $n$ objects, taken $r$ at a time	(r) $_{n} P_{r} / r$
(D) Same as C but identify clockwise with anticlockwise	(s) $3^{n} - 1$
	(t) $2^{n} - 1$

Mathematics - Permutation & Combination Question with Solution | TestHub

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