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Question

In a math class of 30 students, 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.

Accepted Answer

We can choose 2 freshmen girls and 3 freshman boys in 122113 = 10890 ways. There are a total of 305 = 142506 possible groups of 5 students we can choose. Thus the probability of selecting a group of 5 students with 2 freshman girls and 3 freshmen boys is 10890142506 0.076.