# Probability QuestionWatch

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#1

I don't understand why the first answer has "x6"
Also I don't understand how part b was worked out. Any help would be appreciated
0
4 months ago
#2
The 6 will be the nCr term, i.e. the order of the balls do not matter and there are 6 orderings of 3 objects in a group of 3.

For b) the 3 is similar, in a group of 3 objects, two are the same and the other is different, there are 3 different ways of getting it. The 2/8 is the prob of selecting a ball of the same colour (2 out of 8) and the 6/7 is the prob of a different colour, given that two balls of the same colour have already been taken.

(Original post by Annonymous0932)

I don't understand why the first answer has "x6"
Also I don't understand how part b was worked out. Any help would be appreciated
0
#3
(Original post by mqb2766)
The 6 will be the nCr term, i.e. the order of the balls do not matter and there are 6 orderings of 3 objects in a group of 3.

For b) the 3 is similar, in a group of 3 objects, two are the same and the other is different, there are 3 different ways of getting it. The 2/8 is the prob of selecting a ball of the same colour (2 out of 8) and the 6/7 is the prob of a different colour, given that two balls of the same colour have already been taken.
Oh right, thank you. We have never used nCr in probability so I think this isn't on my spec
0
4 months ago
#4
Its just a shorthand way of saying you need to consider the number of combinations of the objects.
So for the first one, you could have
RGB,RBG,BRG,BGR,GBR,GRB
All would have the same probability of 3/56 so the probability of getting 3 different colours is 6*3/56 = 9/28,

(Original post by Annonymous0932)
Oh right, thank you. We have never used nCr in probability so I think this isn't on my spec
0
4 months ago
#5
(Original post by Annonymous0932)
Oh right, thank you. We have never used nCr in probability so I think this isn't on my spec
nCr is a quicker way than sketching out a tree diagram.
If you drew such a diagram then you'd see why there are 6 out of the 27 possible routes being selected.
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