Problem

The editorial staff at a magazine company is reviewing 16 articles. They wish to select seven for the next issue of the magazine, and must also decide in what order the stories will appear. If it takes 1 minute to write a list of seven articles selected for the magazine, how many years would it take to write all possible lists of seven articles? Assume 60 minutes in an hour, 24 hours in a day, and 365 days in a year.

Answer

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Answer

Rounding to one decimal place, it would take approximately \(\boxed{109.7}\) years to write all possible lists of seven articles.

Steps

Step 1 :Given that there are 16 articles and we need to select 7 of them in a specific order, we are looking for the number of permutations of 16 articles taken 7 at a time. The formula for permutations is given by \(nPr = \frac{n!}{(n-r)!}\).

Step 2 :Substituting the given values into the formula, we get \(16P7 = \frac{16!}{(16-7)!} = 57657600.0\) permutations.

Step 3 :Assuming it takes 1 minute to write a list of seven articles, the total time in minutes it would take to write all possible lists is equal to the total number of permutations, which is 57657600.0 minutes.

Step 4 :We know that there are 60 minutes in an hour, 24 hours in a day, and 365 days in a year. Therefore, there are \(60 \times 24 \times 365 = 525600\) minutes in a year.

Step 5 :To find out how many years it would take to write all possible lists, we divide the total time in minutes by the number of minutes in a year. So, \(\frac{57657600.0}{525600} = 109.6986301369863\) years.

Step 6 :Rounding to one decimal place, it would take approximately \(\boxed{109.7}\) years to write all possible lists of seven articles.

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