Question

A round table conference is to be held between delegates of 15 companies. In how many ways can they be seated if delegates from two MNCs may wish to sit together?
A) 13! × 2!
B) 14! × 2!
C) 14!
D) 13!

Answer 1

Hint: A round table conference is held between 15 companies. There are 15 delegates and two delegates always wish to be seated together. So consider the two persons as 1 entity and the total persons become 14. Find the arrangement for 14 persons in which 1 entity is considered as two persons.

Complete step-by-step answer:
We are given that a round table conference is to be held between 15 delegates and we have to find out how many ways they can be seated if two delegates wish to sit together.
Total no. of delegates=15
2 delegates wish to sit together so consider them as 1.
Now, total no. of delegates =14
14 persons can be seated in $ \left( {n - 1} \right)! $ ways where n=14.
 $
  \left( {n - 1} \right)! \\
   = \left( {14 - 1} \right)! \\
   = 13! \\
   = 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \\
   = 6227020800 \\
  $
And the two persons who are considered as one can be seated in 2! ways.
Therefore, the delegates can be arranged in $ 13! \times 2! $ ways.
Therefore, from among the options given in the question Option A is correct, which is $ 13! \times 2! $
So, the correct answer is “Option A”.

Note: A permutation is arranging the objects in order. Combinations are the way of selecting the objects from a group of objects or collection. When the order of the objects does not matter then it should be considered as Combination and when the order matters then it should be considered as Permutation. Do not confuse permutation with combination.