SOLUTION: In a math class, 12 out of 15 girls are fourteen years old and 11 out of 15 boys are fourteen years old. What is the probability of selecting a group of five students

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Question 616248: In a math class, 12 out of 15 girls are fourteen years old and 11 out of 15 boys are fourteen years old. What is the probability of selecting a group of five students - 2 fourteen year old girls and 3 fourteen year old boys? (Explaining the process would be helpful too!)
Answer by stanbon(75887) (Show Source):
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In a math class, 12 out of 15 girls are fourteen years old and 11 out of 15 boys are fourteen years old. What is the probability of selecting a group of five students - 2 fourteen year old girls and 3 fourteen year old boys? (Explaining the process would be helpful too!)
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# of ways to pick a pair of 14-yr old girls: 12C2 = 66
# of ways to pick a triple of 14 years old boys: 11C3 = 165
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# of ways to meet the given condition for the group of 5)= 65*165
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# of random number of groups of 5 students: (12+15)C5 = 27C5 = 80730
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P(meet conditions) = (65*165)/80730 = 0.1329..
Cheers,
Stan H.

SOLUTION: In a math class, 12 out of 15 girls are fourteen years old and 11 out of 15 boys are fourteen years old. What is the probability of selecting a group of five students - 2 fourteen