Perms and combs question (1 Viewer)

[jeffwu95]

In how many ways can 5 men and 5 women be arranged in a circle so that the men are separated? In how many ways can this be done if two particular women must not be next to a particular man?

I need help with the second part

 

[RealiseNothing]

Seat the 'particular man', then seat two females on either side of him that aren't the 'particular women'. Then just arrange the rest however.

 

[jeffwu95]

i attempted to do that, and also included if there was just one woman, but i dont get the answer

 

[RealiseNothing]

i attempted to do that, and also included if there was just one woman, but i dont get the answer

What did you get and what is the actual answer?

 

[jeffwu95]

The answer is 864

 

[RishBonjour]

I did it this way (NOTE, i just started this topic last week, so might be wrong working, but seems logical):

consider the 'particular man' sitting first:

1

now, 2 women can't sit next to him, thus, 3 women can so

1x3x2 (3 choices for one side, and 2 choices for the other)

Now, there are 4 men left and 3 women left who must alternate
hence 4! x 3! ways of arranging them

so finally

1x3x2 x4! x 3! = 864

 

[jeffwu95]

I did it this way (NOTE, i just started this topic last week, so might be wrong working, but seems logical):

consider the 'particular man' sitting first:

1

now, 2 women can't sit next to him, thus, 3 women can so

1x3x2 (3 choices for one side, and 2 choices for the other)

Now, there are 4 men left and 3 women left who must alternate
hence 4! x 3! ways of arranging them

so finally

1x3x2 x4! x 3! = 864

Thanks! so smart (y)