Question

in how many different arrangements can 5 men and 5 women sit around a circular table so that no two men sit together ​

Answer 1

Step-by-step explanation:

In a Circular arrangement, Total Permutation is (n-1)!

Here we don't want women to sit together, hence we follow these steps.

Step1: Fix all the boys first around the table. This can be done in (5-1)!

Step2: Now we have 5 places inbetween these men where we can fit available 5 Women. This can be done in 5! Ways.

Total number of ways = 4! x 5!

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i hope it will helps you friend

Answer 2

Ello user !!!!!

Here is your answer,

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Lets first place the men (M). '*' here indicates the linker of round table

* M -M - M - M - M *

which is in (5-1)! ways  

So we have to place the women in between the men which is on the 5 empty seats ( 4 -'s and 1 linker i.e * )

SO 5 women can sit on 5 seats in (5)! ways or  

1st seat in 5 ways

2nd seat 4

3rd seat 3

4th seat 2

5th seat 1

i.e 5*4*3*2*1 ways  

So the answer is 5! * 4! = 2880

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HOPE THIS HELPS YOUU :)

AND STAY BLESSED.