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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?

 May 27, 2020
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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

...

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

...

66*165/142506=10890/142506, which is 605/7917.

 

---Tom

 May 27, 2020

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