The text states:

There are 3 seniors and 15 juniors in Mrs. Gillis’s math class. Three students are chosen at random from the class. What is the probability that the group consists of a senior and two juniors?

I answered this correctly by using Combinations to calculate the number of elements in the sample space (816) and the number of possible combinations of one senior and two juniors (315), arriving at a probability of 38.6%, which is the answer the text gives.

However it seems like another way to answer the question is to calculate the probability of selecting 1 senior out of 3 (3/18) and multiply by the probability of picking 1 junior out of the 17 remaining students (15/17) and multiply that by the probability of choosing another junior out of the remaining 16 students (14/16). Yet this results in a different answer: 12.86%

What have I missed?


What you've calculated is the probability of choosing first a senior and then two juniors. This is one third of the probability that you're looking for, since you can also choose first a junior, then a senior, then another junior, or first two juniors and then a senior, and these three possibilities are all equally likely.


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