SOLUTION: There are 100 students that are randomly placed into 4 classrooms. Three students want to be in the same class. Probability they are in the same class? probability they are all P's

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Question 245300: There are 100 students that are randomly placed into 4 classrooms. Three students want to be in the same class. Probability they are in the same class? probability they are all P's class? Probability they are all in different classes?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There are 100 students that are randomly placed into 4 classrooms.
Three students want to be in the same class.
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Probability they are in the same class?
Pick a classroom: 4 ways
Place the 3 randomly: 100*99*98 ways
Probability 4/(100*99*98) = 0.000004123
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probability they are all in P's class?
# of ways to succeed: 1 way
# of ways to place randomly: 100*99*98
Probability = 1/970200
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Probability they are all in different classes?
Pick 3 classes: 4C3 = 4
Put the 3 students in the three classes: 3*2*1 = 6
probability (4*6)/970200 = 0.00002474
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Cheers,
Stan H.