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Can someone please tell me what \(C^3_8\) means in the answer below:
Bunuel wrote:
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.
[/quote]
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Can someone please tell me what \(C^3_8\) means in the answer below
\(C^3_8\) 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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