Question:

$20$ persons are invited for a party In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

Updated On: Jul 2, 2022
  • $20!$
  • $ 2 \times 18!$
  • $ 18!$
  • None of these
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The Correct Option is B

Solution and Explanation

There are total $20 + 1 = 21$ persons. The two particular persons and the host be taken as one unit so that these remain $21 - 3 + 1 = 19$ persons be arranged in round table in $18!$ ways. But the two persons on either sides of the host can themselves be arranged in $2!$ ways. $\therefore$ Required number of ways $= 2! \times 18! = 2 \times 18! $
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Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.