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Match the following:
There are 2 Indian couples, 2 American couples and one unmarried person
Column I Column II
(A) The total number of ways in which they can sit in a row such that an Indian wife and an American wife are always on either side of the unmarried person, is (P) 22680
(B) The total number of ways in which they can sit in a row such that the unmarried person always occupies the middle position, is (Q) 5760
(C) The total number of ways in which they can sit around a circular table such that an Indian wife and an American wife are always on either side of the unmarried person, is (R) 40320
(D) If all the nine persons are to be interviewed one by one, then the total number of ways of arranging their interviews such that no wife gives interview before her husband, is (S) 24320

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$(A) \to (R), (B) \to (Q), (C) \to (S), (D) \to (P)$

$(A) \to (Q), (B) \to (S), (C) \to (R), (D) \to (Q)$

$(A) \to (R), (B) \to (R), (C) \to (Q), (D) \to (P)$

$(A) \to (S), (B) \to (P), (C) \to (P), (D) \to (Q)$

answer is D.

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Detailed Solution

A) One Indian wife and one American wife can be selected in $2_{C_{1}} \times 2_{C_{1}}$ ways and keeping an unmarried person in between these two wives the total number of linear arrangements are $2_{C_{1}} \times 2_{C_{1}} \times 7 \times 2 = 40320$
B) Required number of ways $= 8 = 40320$
C) Required number of ways $= (7 - 1) \times 2 \times 2_{C_{1}} \times 2_{C_{1}} = 5760$
D) Number of ways in which interviews can be arranged $= 9 \times 8_{C_{2}} \times 6_{C_{2}} \times 4_{C_{2}} \times 2_{C_{2}} = 22680$

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