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?
+298 number of ways to select 2 freshman girls: 12 choose 2
number of ways to select 3 freshman boys: 11 choose 3
using the formula: n!/k!(n-k)!
12 choose 2 is 12!/2!10!, which is 12*11/2, and that is 66
11 choose 3 is 11!/3!8!, which is 11*10*9/6, and that is 165
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number of ways to pick 5 students without restriction: 30 choose 5
30 choose 5 is 30!/5!25!, which is 30*29*28*27*26/120, and that is 142506
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66*165/142506=10890/142506, which is 605/7917.
---Tom
