SOLUTION: I have no idea where to start with this.... Thanks for your help! 11 out of 40 students are selected for a team each year. 15/40 participated once in the last two years. What

Question 329835: I have no idea where to start with this.... Thanks for your help!
11 out of 40 students are selected for a team each year. 15/40 participated once in the last two years. What is the probability of selecting 3 but no more than 5 students from the 15 that previously participated.
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
you want to select n=11 students out of N=40
15 have participated once in the last 2 years, 25 have not
X=# in the 11 which participated previously
You need P(X=3,4 or 5) = P(X=3)+P(X=4)+P(X=5)
There are 40C11 ways to select the 11 students out of 40 =2,311,801,440
There are 15C3*25C8 ways to select 3 students from the 15 who prev participated and 25C8 ways to select 8 students from the 25 that did not = 544*1,081,575 = 492,116,625

P(X=3,4,5) = (15C3*25C8 + 15C4*25C7 + 15C5*25C6)/40C11 =1,680,103,425/2,311,801,440=0.727

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