2010 scegs probability (1 Viewer)

[alexobern]

7a) a Family of six are sitting at a round table.
In how many ways can they be arranged so that Mum and Dad sit together and the youngest daughter, Chelsea, does not sit opposite Dad?

my answer is 36 ways, but i don't have the answers and don't feel confident with it. it's a two marker so shouldn't be too hard... right?

 

[RealiseNothing]

It's 36.

 

[deswa1]

I got 36 as well

 

[scarvesss]

can someone pls explain it a little. idgi

edit: nevermind, didnt realise it was 4u

 

[jeffwu95]

Can someone confirm, im not great at perms and combs
You make the mother a fixed seat as it is a round table so there are 5 seats left, and the father can sit on either seat beside the mother so (times 2)
Excluding the mother, father, and Chelsea there are 3 people left which can occupy the seat opposite to the father so (times 3)
and then the other 3 remaining ppl can rearrange themselves so (times 3!)
so 2.3.3!=36

 

[Sindivyn]

Your Method works
Alternatively, there are 2!*4! ways the table can be arranged without the restriction of the daughter not sitting opposite of the father being in place.
With the restriction that they ARE opposite each other, set the father/ daughter. The mother can go to either side, and the remaining 3 people can fill the remaining 3 slots. That is, 2 * 3!
Combining the two, you get 2!*4! - 2*3! =36