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Yalephd
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Unknown term. 09 Oct 2010, 09:47
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Can someone please tell me what \(C^3_8\) means in the answer below:


Bunuel


A row of seats in a movie hall contains 10 seats. 3 Girls & 7 boys need to occupy those seats. What is the probability that no two girls will sit together?

Consider the following:
*B*B*B*B*B*B*B*

Now, if girls will occupy the places of 8 stars no girl will sit together.

# of ways 3 girls can occupy the places of these 8 stars is \(C^3_8\);
# of ways 3 girls can be arranged on these places is \(3!\);
# of ways 7 boys can be arranged is \(7!\).

So total # of ways to arrange 3 Girls and 7 boys so that no girls are together is \(C^3_8*3!*7!\);
Total # of ways to arrange 10 children is \(10!\).

So \(P=\frac{C^3_8*3!*7!}{10!}=\frac{7}{15}\).

Hope it's clear.
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whiplash2411
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Unknown term. 09 Oct 2010, 09:52
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Quote:
Can someone please tell me what \(C^3_8\) means in the answer below
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\(C^3_8\) refers to combination properties. This basically means the number of ways to pick 3 out of 8 when order does not matter. Permutation would be the case where order matters. I would suggest reading through theMath Book Combinatorics Section
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Unknown term. 09 Oct 2010, 15:20
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\(C_{r}^{n} = \frac{n!}{r!(n-r)!}\)

It is the number of ways to choose r objects from a set of n objects
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Unknown term. 09 Oct 2010, 15:29
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Thanks a lot, whiplash2411 and shrouded1.



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