SOLUTION: In a class containing 10 boys and 8 girls 5 students are chosen (a)what is the probability that at least one girl is chosen (b)what is the probability that all boys will be chos

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Question 298612: In a class containing 10 boys and 8 girls 5 students are chosen
(a)what is the probability that at least one girl is chosen
(b)what is the probability that all boys will be chosen
(c)what is the probability that all girls will be chosen
(d)what is the probability that exactly 2 girls and 3 boys will be chosen
Answer by Jeff Gordon(65) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A-3=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+1.73205080756888
x%5B2%5D+=+%28-%280%29-sqrt%28+12+%29%29%2F2%5C1+=+-1.73205080756888

Quadratic expression 1x%5E2%2B0x%2B-3 can be factored:
1x%5E2%2B0x%2B-3+=+1%28x-1.73205080756888%29%2A%28x--1.73205080756888%29
Again, the answer is: 1.73205080756888, -1.73205080756888. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-3+%29