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a Simple Probability problem

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jas_fluidm:
A university admitted 100 students who transferred from other institutions. Of these students, 34 transferred from two-year community colleges, 25 transferred from private four-year institutions, and the rest transferred from public four-year institutions. If two different students are to be selected at random from the 100 students, what is the probability that both students selected will be students who transferred from two-year community colleges?

Answer:
34/100 * 33/99 = 1122/9900 = 17/150

Another way to solve this problem:

Total combinations of 2 students from 2-year community colleges: 34!/(2!(32!)) = 561

Total combinations of 2 students from all 100 students: 100!/(2!(98!)) = 4950

Then the probability is 561/4950 = 17/150

arefin:
Thanks.

Sima:
It's a mathematical approach and it is the problem of conditional probability in statistical approach.

jas_fluidm:
thanks for the comment

tasnuva:
Thanks.

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