An art gallery has reserved ten locations for Maggie's show. Maggie has ten paintings but is uncertain how to display them. She insists on trying every possible arrangement before making her decision! If she takes 1 minute to set up and view each arrangement and works 10 hours a day for 6 days a week, how many years will it take her to decide?

To find out how many years it will take Maggie to decide on the arrangement for her paintings, we need to determine the total number of arrangements and calculate the time it will take her to go through all of them.

Maggie has 10 paintings, and 10 locations are reserved for her show. The total number of arrangements can be calculated using the concept of permutations, which is denoted by "nPr". The formula for permutations is:

nPr = n! / (n - r)!

where "n" is the total number of items and "r" is the number of items selected at a time. In Maggie's case, n = 10 (paintings) and r = 10 (locations), so the formula becomes:

10P10 = 10! / (10 - 10)! = 10! / 0! = 10!

Now, let's calculate 10!:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

So, there are 3,628,800 different arrangements possible for Maggie's paintings.

Maggie takes 1 minute to set up and view each arrangement. If she works 10 hours a day for 6 days a week, the total number of minutes she works in a week can be calculated as:

Total work minutes per week = 10 minutes/hour x 10 hours/day x 6 days/week = 600 minutes/week

Now, let's calculate how many weeks it will take her to go through all the arrangements:

Number of weeks = (Total number of arrangements) / (Total work minutes per week)

Number of weeks = 3,628,800 / 600 = 6,048

Finally, let's calculate how many years it will take Maggie:

Number of years = Number of weeks / 52 (assuming there are 52 weeks in a year)

Number of years = 6,048 / 52 = 116.31

Therefore, it will take Maggie approximately 116.31 years to try every possible arrangement before making her decision for the art gallery show.