Q.

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

(A)  (R), (B)  (Q), (C)  (S), (D)  (P)

b

(A)  (Q), (B)  (S), (C)  (R), (D)  (Q)

c

(A)  (R), (B)  (R), (C)  (Q), (D)  (P)

d

(A)  (S), (B)  (P), (C)  (P), (D)  (Q)

answer is D.

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Detailed Solution

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A) One Indian wife and one American wife can be selected in 2C1×2C1 ways and keeping an unmarried person in between these two wives the total number of linear arrangements are  2C1×2C1×7×2=40320
B) Required number of ways  =8=40320
C) Required number of ways  =(71)×2×2C1×2C1=5760
D) Number of ways in which interviews can be arranged  =9×8C2×6C2×4C2×2C2=22680

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