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In how many ways can 10 engineers and 4 doctors be seated at a round table if no two doctors sit together?

A.

10!×4!

B.

9!×9!× ^{10}P_{4}

C.

10!×10!× ^{10}P_{4}

D.

13!

Answer with explanation

Answer: Option BExplanation

No two doctors sit together. Hence, let’s initially arrange the 10 engineers at a round table. Number of ways in which this can be done =(10−1)!=9!=(10−1)!=9! …(A)

Now there are 10 positions left (marked as *) to place the 4 doctors as shown below so that no two doctors can sit together.

Number of ways in which this can be done

= ^{10}P_{4} …(B)

From (A) and (B),

Required number of ways =9!×=9!× ^{10}P_{4}

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