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Probability low to charge that instead of using random selection

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A certain company reduced its management staff from 20 managers to 16. The company claimed that four managers were randomly selected for job termination. However, the four managers chosen are the four oldest managers among the 20 that were employed. Answer the questions below.

a. Find the probability that when four managers are randomly selected from a group of 20, the four oldest are selected ______________(type as an integer or a simplified fraction.

b. Is that probability low enough to charge that instead of using random selection, the company actually fired the oldest employees?

(A). Yes, the probability is low enough, therefore, it is possible that the oldest employees were randomly selected.
(B. )No, because it would not be unusual to fire the oldest managers, given that they were randomly selected for termination.
(C.) No, the probability is not low. Each manager had an equal chance of being fired.
(D.) Yes, because it would be unusual to fire the oldest managers, if they were really randomly selected for termination.

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Solution Summary

The probability low enough to charge that instead of using random selection is determined.

Solution Preview

a) There are a total of 20 managers, Thus there are a total of (20 C 4) = 4845 ways ...

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