Probability question help please (1 Viewer)

[Elise8842]

Hi

I got a different answer (which quite makes sense) , could someone tell me why I'm wrong?

To make it correct, The only way is to subtract 12 in my answer .... But, the function C doesn't consider order, isn't it?!
Only the P function counts different orders , so what's happening here????!!!!

Someone....help....please.....

~

 

[faisalabdul16]

The question says exactly one couple, therefore you have 4 to choose from. Then the remaining 2 people can be chosen in 6C2 ways (as there are 6 people) however multiplying these two won't give the correct answer because you can choose 2 people who ARE a couple which means there will be 2 couples and therefore going against the question (not answering it). From the 6C2 ways, 3 MUST be deducted because you can choose couple B,C or D when couple A has already be chosen and the question is saying exactly one couple. Hence 4x(6C2-3)

Soz if u didn't understand this.

 

[braintic]

Two errors:

(1) Why did you multiply by 4C2? It should be 6C2 - you are choosing 2 from 6.

(2) Although there are 6 ways of choosing a pair of couples, your method involves double counting all such pairs.
If A and B are a couple, and so are C and D, you are picking AB and CD
(i) by picking AB as the initial pair, then picking C and D separately
(ii) by picking CD as the initial pair, then picking A and B separately

So the calculation is 4 times 6C2 - 2 times 6 = 48