The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

  • Option 1)

    30

  • Option 2)

    5!\times 4!

  • Option 3)

    7!\times 5!

  • Option 4)

    6!\times 5!

 

Answers (1)

As we learnt in

Conditions for Circular Permutation -

The number of circular permutations of n distinct things = (n - 1)!

-

 

 6 Men and 5 Women can dine at a round table. 

6 Men can dine in 5! ways.

 and 5 Women can choose from 6 places in ^{6}C_{5}\ ways

and dine in 5! ways.

Number of ways = =5!\times6\times 5!=5!\times 6!

Correct option is 4.

 

 


Option 1)

30

This is an incorrect option.

Option 2)

5!\times 4!

This is an incorrect option.

Option 3)

7!\times 5!

This is an incorrect option.

Option 4)

6!\times 5!

This is the correct option.

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