gmatpapa: As per your request, let me try to explain you the logic here.
Look at the question: "what is the probability that the 2
students selected will be a set of lab partners"
So you see 2 students in front of you - one from freshmen class and the other from sophomore. What is the probability that they are lab partners? There are only 75 pairs of lab partners possible. Total possible pairs are 600*900 (600C1 * 900C1)
So probability = 75/54000 = 1/7200
When you have a question similar to 'There are 4 boys and 3 girls. In how many ways can you make a pair of one boy and one girl?', what do you do? You say we can pick a boy in 4 ways and a girl in 3 ways so total 12 ways.
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B G
There is one spot for a boy and one for a girl. Their positions are defined. As if there were two chairs, a blue one and a pink one for the boy and the girl respectively. So you don't arrange them. You fill the blue chair and the pink one. You don't say "we pick the boy first and then the girl or girl first and then the boy so we get 2 cases, right?"
It is a situation similar to this situation.
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Karishma
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