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In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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17 Mar 2011, 06:33

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In a high school debating team consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors, two students are selected to represent the school at the state debating championship. The rules stipulate that the representatives must be from different grades, but otherwise the 2 representatives are to be chosen by lottery. What is the probability that the students selected will consist one freshman and one sophomore?

Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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17 Mar 2011, 07:04

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Total number of ways to select 2 students from any two groups =

\(C^4_2*C^2_1*C^2_1 = 4*(3/2)*2*2 = 24\)

\(C^4_2\) -- Number of ways to select 2 groups out of 4 groups \(C^2_1\) -- Number of ways to select 1 student from 1 of the selected groups \(C^2_1\) -- Number of ways to select 1 student from 2nd selected group

There are total 24 ways in which you can select two students from any two groups.

Selecting 2 students, one each from freshmen and sophomore = \(C^2_1*C^2_1=2*2=4\)

Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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