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In a sociology class there are 14 sociology majors and 10 non-sociology majors. 3 students are randomly selected to present a topic. What is the probability that at least 2 of the 3 students selected are sociology majors?

Mar 5, 2020

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You are choosing 3 out of 24 students = 24C3.

Either 2 of the 14 sociology students = 14C2 and 1 of the 10- non-sociology students = 10C1

or       3 of the 14 sociology students = 14C3 and none of the 10- non-sociology students = 10C0.

[ 14C2 x 10C1  +  14C3 x 10C0 ] / 24C3

=  [ 91 x 10  +  364 x 1 ] / 2024

=  [ 910 + 364 ] / 2024

=  1274 / 2024

Mar 5, 2020
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