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A wedding organizer needs to sit 4 couples and 4 single persons around a round table....

A wedding organizer needs to sit 4 couples and 4 single persons around a round table. In how many ways can she sit those 12 people so that:

(a) All couples sit together (the two members of each couple sit side-by-side)?

(b) No couple sit together? Hint: Inclusion-Exclusio

Note: Since the table is round, different rotations of the same arrangement are indistin- guishable, but a clockwise arrangement is distinguishable from its counterclockwise version.

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