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?
+23246 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
