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A person hosts a party of 13 guests and places 5 of them on one table and the remaining on the other table, the tables being round. In how many ways can he arrange the guests?

Question and options

A person hosts a party of 13 guests and places 5 of them on one table and the remaining on the other table, the tables being round. In how many ways can he arrange the guests?
  1. 13!40\frac{13!}{40}
  2. 13!5!8!\frac{13!}{5!8!}
  3. 13!4!7!\frac{13!}{4!7!}
  4. 13!80\frac{13!}{80}

Answer and explanation

Correct answer: A - \(\frac{13!}{40}\)
Choose 5 guests: C(13,5); circular arrangements 4! and 7!. Total = 13!/(5!8!) x 4! x 7! = 13!/(5x8) = 13!/40.

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