Strangely Hard Perms/Combs Question (1 Viewer)

[hornsbystudylad]

I get the first part, NOT THE SECOND.

I tried 9! - 7! x 2, which was 352800.
I then tried total arrangments + 7! x 2 - (both cases of one woman next to man) because I assummed that both women could not be beside the man solo as well. That got me 211680.
Answer is 864.

Please help me understand (this is a plea my exam is tmrw).

[feel free to use this thread to post ur own perms and comms queries god that topic is so aids]

 

[jimmysmith560]

There is a very similar version of this question, the only difference being that men and women are replaced by writers and artists respectively, as follows:

"In how many ways can five writers and five artists be arranged in a circle so that the writers are separated? In how many ways can this be done if two particular artists must not sit next to a particular writer?"

The following is an approach to the second part of this question that was posted in an older thread:

It's exactly as it says: two particular artists aren't allowed to sit next to a writer, for whatever reason - perhaps they insulted each other's artworks.
It is actually fairly simple:

Step 1: Arrange the 5 writers first. Simple, just 4! = 24.

Step 2: You might like to draw a pentagon to visualise this. The vertices of the pentagon will represent the writers, the sides the artists. Circle any of the vertices of the pentagon, and let this particular point be the 'particular writer', which I'll call Fred. So, if the writers and artists must continue to be separated, then the logical conclusion is that the two artists, which we'll call A and B, cannot be on the sides with that vertex. There are then only 3 sides of the pentagon that A and B can occupy, since they despise Fred. Choose 2 of these sides - . Arrange them in 2! ways, and multiplying gives 6, which is .

Step 3: Order the rest of the artists - 3! = 6 ways.
Multiply together to get 864.

I hope this helps!

 

[Lith_30]

I think you misinterpreted the question, it was asking for how many ways you could keep the two women separated from the man, while they are also arranged in alternating order.

I think the best way to start is to find the arrangements just for the men in a circle which is 4!, given that one man is does not move.


Then we shall place the women in between the arrangement of men, lets start with the women that cannot sit next to the man.
There are three spots for the first woman that cannot sit next to the man (as the other two are next to the man), then the other woman has only two spots left to sit.
Finally the rest of the women can sit in the remaining seats which give 3! arrangements

Therefore the total arrangements possible is

 

[hornsbystudylad]

There is a very similar version of this question, the only difference being that men and women are replaced by writers and artists respectively, as follows:

"In how many ways can five writers and five artists be arranged in a circle so that the writers are separated? In how many ways can this be done if two particular artists must not sit next to a particular writer?"

The following is an approach to the second part of this question that was posted in an older thread:



I hope this helps!

jimmy I need your autograph - you're just everywhere man, thanks for the help!

 

[jimmysmith560]

jimmy I need your autograph - you're just everywhere man, thanks for the help!

No worries man! If you come to the BoS meet up, then I can get yours too