Problem

Three current employees and eight noncurrent employees are waiting to be interviewed for jobs. If they are all selected in random order, find the probability that all current employees will be interviewed first.

Answer

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Answer

\(\boxed{0.00606}\) is the final answer. This is the probability that all current employees will be interviewed first.

Steps

Step 1 :There are three current employees and eight noncurrent employees waiting to be interviewed for jobs. They are all selected in random order.

Step 2 :We need to find the probability that all current employees will be interviewed first.

Step 3 :The total number of ways to arrange the interviews is the number of permutations of 11 people, which is \(11!\).

Step 4 :The number of ways to arrange the interviews such that all current employees are interviewed first is the number of permutations of 3 people (the current employees) times the number of permutations of 8 people (the noncurrent employees), which is \(3! * 8!\).

Step 5 :The probability is then the number of favorable outcomes divided by the total number of outcomes.

Step 6 :The total number of outcomes is \(39916800\).

Step 7 :The number of favorable outcomes is \(241920\).

Step 8 :The probability is \(0.006060606060606061\).

Step 9 :\(\boxed{0.00606}\) is the final answer. This is the probability that all current employees will be interviewed first.

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