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Chapter 5: Problem 46

A company employs a total of 16 workers. The management has asked these employees to select 2 workers who will negotiate a new contract with management. The employees have decided to select the 2 workers randomly. How many total selections are possible? Considering that the order of selection is important, find the number of permutations.

Short Answer

Expert verified
The total number of selections (combinations) is 120 and the number of permutations is 240.

Step by step solution

01

Combinations

Start by calculating the number of combinations by using the given formula. Here, n = 16 (total workers) and r = 2 (the ones to be selected). Substituting these into the formula we have \(_{16}C_2 = \frac{16!}{2!(16-2)!}\). Calculate 16! and (16-2)! separately then plug the calculations into the formula to find the total number of selections (i.e., combinations).
02

Permutations

Next, find the number of permutations using the formula. As before, n = 16 and r = 2. Substituting these into the formula we have \(_{16}P_2 = \frac{16!}{(16-2)!}\). The calculation of 16! would already be done from Step 1, so you only have to calculate (16-2)! again separately. Plug the calculations into the formula afterwards to find the number of permutations.

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