SOLUTION: In a math class, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. What is the probability that in a randomly selected group of five students from the class, ther

Question 249154: In a math class, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. What is the probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys? Express your answer as a decimal to the nearest thousandth.
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a math class, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. What is the probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys? Express your answer as a decimal to the nearest thousandth.
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# of ways to select 2 freshman girls: 12C2
# of ways to select 3 freshman boys: 11C3
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# of ways to pick 5 students without restriction: 30C5
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P(2 frosh girls and 3 frosh boys) = [12C2*11C3]/30C5 = [66*55]/142506=0.0255
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Cheers,
Stan H.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
nCr = n!/((n-r)!r!) Combination of n things taken r at a time.
.
12C2 twelve frosh girls taken 2 at a time= 66 different combinations.
11C3 eleven frosh boys taken 3 at a time= 165 different combinations.
30C5 Thirty students taken 5 at a time=142506 different combinations.
.
(66*165)/142506
=.076
.
Ed
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