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In this problem, it is said that a company hires at random five engineers from its pool of 10 applicants.
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In this pool, there are seven electrical engineers and three computer engineers.
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We need to find the probability that exactly two of the hired applicants are electrical engineers.
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Now, the required probability is the number of favorable outcomes divided by the total number of outcomes.
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First of all, let us consider the total number of outcomes, which we write in the denominator here.
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Now there is a pool of 10 applicants, and out of those 10 applicants, any 5 need to be selected at random.
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This can be done in 10c5 ways.
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Here we use c, which represents combination, and we use combination and not permutation in this case, because the order of selection of the applicants does not matter.
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So that's the total number of outcomes.
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Next, consider the number of favorable outcomes, which we write in the numerator here.
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Now, we want to find the probability that exactly two of the hired applicants are electrical engineers.
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So the number of favorable outcomes will be the number of ways that the five applicants can be hired so that exactly two of them are electrical engineers...