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Question

The 10 students of Batch B feel they have some conceptual doubt on ‘Circular Permutation’. Mr. Sood called them in discussion room and asked them to sit down around a circular table which is surrounded by 13 chairs. Mr. Sood told that his adjacent seat should not remain empty. The number of ways in which the students can sit around a round table if Mr. Sood also sits on a chair is


A

C210×C810

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B

C210×2!×C810×8!

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C

C310×3!×C710

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D

None of these

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Solution

The correct option is B

C210×2!×C810×8!


Explanation for the correct option:

Step 1. Find number of ways the students can sit adjacent to the teacher

Given:

Number of chairs =13

Number of students =10

Number of teacher=1

According to the question,

The adjacent two seats to the teacher should not be empty

Then out of 10 students , the number of ways to choose two students who will sit in these adjacent seats =C210×2! ways

Step 2. Find required number of possible ways:

Now, for rest of the 10 chairs and 8 students, total number of possible ways =C810×8!

The number of ways students can sit around the table =C210×2!×C810×8!

Hence, Option ‘B’ is Correct.


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