SOLUTION: There are 26 students in a class of which 14 are science majors. If a sample of 5 students is selected. Find the probability that 3 are science majors.

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Question 1176469: There are 26 students in a class of which 14 are science majors. If a sample of 5 students is selected. Find the probability that 3 are science majors.

Answer by greenestamps(13200) About Me  (Show Source):
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Use the basic definition of probability:
                          number of desirable outcomes
  P(desired outcome) = ---------------------------------
                       total number of possible outcomes

The total number of possible outcomes is the number of ways of choosing 5 of the 26 students on the class: 26 choose 5.

The number of desirable outcomes is the number of ways of choosing 3 of the 14 science majors AND 2 of the other 12 students: (14 choose 3) times (12 choose 2). Note the AND means those two numbers of ways get multiplied.

So the probability that 3 of the 5 chosen are science majors is

%28C%2814%2C3%29%2AC%2812%2C2%29%29%2FC%2826%2C5%29

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