Job Applications Ten people apply for a job at Computer...

Job Applications Ten people apply for a job at Computer
Warehouse. Five are college graduates and five are not.
If the manager selects 3 applicants at random, find the
probability that all 3 are college graduates.

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Key Concepts

Sampling Without Replacement

Sampling without replacement refers to the process of selecting items from a group where each item can only be chosen once. This concept is fundamental in the problem since, once an applicant is selected, they are not returned to the pool, thereby affecting the probability of subsequent selections.

Combination Formula

The combination formula, given by C(n, k) = n! / (k!(n - k)!), is used to calculate the number of ways to choose k items from a total of n items without regard to the order. This formula is crucial in computing the number of groups (or sets of individuals) possible in situations where the arrangement is irrelevant.

Probability

Probability is a measure of the likelihood of an event occurring, often calculated as the ratio of favorable outcomes to the total number of possible outcomes. In this context, it involves determining how likely it is to select three college graduates when the selection is made randomly from a mixed group.

Combinatorial Analysis

Combinatorial analysis involves counting and enumerating possibilities, which is essential for problems where order does not matter. It provides the techniques, such as using combinations, to calculate the number of ways events can occur, helping in determining both the favorable and the total outcomes.

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