Permutations question (2 Viewers)

[lyounamu]

In how many ways can 5 men and 5 women by 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 did this question and I got them all right. But I want to know what the model working out would look like. That is because I haven't provided any explanation lines in my working out. I just jotted down the working out like: 5! x 4! for the first part and I got the answer. But I don't think it will be acceptable in exam. Can anyone write full working out for this?

For your info, answers are 2880 and 864, both of which I got. I just find it difficult to write working out for permutation question. Help is greatly appreciated.

 

[lolokay]

how much working would you need?
first one: keep one, say, man stationary. order the remaining 5 women and 4 men = 5!4!

second one: keep the man stationary. order the other 4 men. order the 2 women that can't sit next to the first man in the other 3 spots. order the remaining 3 women = 4!3!3!

 

[PC]

PERFECT working would be something like:

(a) Number of ways = 5! x 4!
= 2880

(b) Number of ways = 4! x 3! x 3!
= 864

In other words, make sure your answers are labelled clearly using the nomenclature of the question (i.e. (i), (ii), (a), (b), etc). State clearly and briefly what you're trying to find, in this case "number of ways". Make sure the "=" signs are underneath each other. I can't think of anything else. You're only asked to work out the answer, not to explain why, so you don't have to provide a written paragraph.

 

[lyounamu]

Thanks to both. So we don't need like big paragraph explaining everything? I basically did what you guys did. So I guess it's satisfactory. Thanks.